DEPLOYMENT ORDER

Deployment order is very important here.
All three Dawn Office IDs need to be on-field at encounter start to get the full Dawn Office buff (it will be stuck at below 3 if not everyone is there at start), so not all Thumb IDs can be there from the start. [Meursault] The Thumb East Capo IIII is chosen to be there in order to give him time to pop [Meursault] Crushbound Past early (12 turns of Accumulated Past will give 3 clash power) and the rest of his EGO Passives (with [Meursault] Regret also being very important), as well as to start spending his bullets. [Ryōshū] Blade of the House of Spiders will spend 3 turns killing the rest of the House of Spiders IDs, excluding [Rodion] The House of Spiders: The Thumb Nursefather and [Heathcliff] The House of Spiders: The Thumb Apprentice, who are both set as last to deploy for this reason. The first sinner [Ryōshū] Blade of the House of Spiders kills needs to be a Nursefather, to make her kill two sinners at a time afterwards, and for this I chose [Hong Lu] The House of Spiders: The Ring Nursefather because of his low starting damage and being unaccompanied by his Apprentice, though this can be changed according to the taste of the user, if you think a different deployment order is better.

This deployment order doesn't take into account Mirror Dungeon EGO Gift usage.

SELECTED EGOS REASONING

EGOs chosen here mainly focus on synergy with Burn, Tremor and each individual ID's strengths and sin affinities.

• Faust naturally uses [Faust] Everlasting in her WAW slot. For her TETH slot I chose [Faust] Hex Nail instead of [Faust] Lasso because using Lasso to try to give her Haste to try and use Everlasting is not worth it and not needed; she has enough speed on her own. For her HE slot I chose [Faust] Ardor Blossom Star because of synergy with Burn, but if you have access to collab EGOs, definitely use [Faust] Command : Meltdown. Faust generates enough Gluttony resource to use it with her follow up attack. Otherwise, you can use another healing ego, such as [Faust] Fluid Sac or [Faust] Thoracalgia if you are confident that you'll have enough EGO resource. The team does have enough Pride Resonance to make use of Thoracalgia.
• Ryōshū is mostly self-explanatory. I did not use [Ryōshū] Blind Obsession or [Ryōshū] Thoracalgia because she already has enough Poise sustain without them. [Ryōshū] 4th Match Flame is there to enhance damage, and if threadspun to tier V it also supports [Ryōshū] Great Trichiliocosm [三千大世界] a lot.
• Meursault is also simple - these EGOs have very powerful passives. [Meursault] Pursuance can be exchanged for [Meursault] Capote, but Capote's passive isn't very powerful/consistent when Meursault isn't going solo.
• Heathcliff uses [Heathcliff] Move-in Reg. for synergy with Burn. [Heathcliff] Asymmetrical Inertia is chosen for the very useful passive of inflicting Fragile with Tremor Burst, but using [Heathcliff] Ya Śūnyatā Tad Rūpam is also an option for powerful SP heals for the team.
• Rodion uses [Rodion] Into the Sunset for the healing and powerful passive. [Rodion] Effervescent Corrosion is there for the great initial Tremor Count infliction, but can be hard to use right away with the meager Gluttony resource. [Rodion] Pursuance is there for the powerful healing and clashing. As of making this guide, Threadspin V [Rodion] 4th Match Flame hasn't been released or even teased yet, so that may turn out better.
• Sinclair uses [Sinclair] Cavernous Wailing to make use of the sizeable shield amount he gets from the From Dawnbreak to Sunset buff. [Sinclair] Impending Day's passive allows for a lot of extra resource generation (replaces [Sinclair] Lantern because there's already a lot of healing EGOs on the team and very little Gluttony, but can be exchanged back), while [Sinclair] Harmony is basically tailor-made to help [Sinclair] Dawn Office Fixer manage his SP. Using [Sinclair] Tears of the Tarnished Blood [汚血泣淚] is actually not recommended unless Sinclair is close to death with no chance of healing for whatever reason.
• Gregor doesn't have many important EGOs, unless you have access to [Gregor] Unbrilliant Glory, which is perfect for him in this team. [Gregor] Bygone Days is used instead of [Gregor] Lantern because of Gregor already being able to heal himself. [Gregor] Solemn Lament makes use of his self-inflicted Burn to get Attack Power Up from the passive. If you don't have [Gregor] Unbrilliant Glory, [Gregor] Garden of Thorns is decent enough to heal the team or get some Sin Affinity buffs, but it can be hard to use it along with a good enough Sin Resonance.
  Sinners without proper EGOs chosen for them are there to be sacrificed to [Ryōshū] Blade of the House of Spiders, but if you wish to change that, feel free.

USING THE TEAM

[Ryōshū] Blade of the House of Spiders focuses on killing the House of Spiders IDs other than the Thumb Duo for the first three turns, so slot in an evade every time. If the evade isn't activated, you can also pass the turn without losing the skill replaced by the evade, if it's something you want to save, like an S3. After all that is done, pop 4th Match Flame if you have it and Great Trichiliocosm [三千大世界] at your leasure. Enjoy the busted damage numbers of Great Trichiliocosm [三千大世界] and Ryōshū's Rend Space - Echoshear [空間斬 - 殘]. Also, if you have options of using Tripleslash - Echoshear [三連 - 殘] or Rend Space [空間斬] on a single target - use Tripleslash - Echoshear [三連 - 殘], it's better for single target damage.
If you're doing Refraction Railway, DON'T kill the HoS IDs if you have other stages coming up where the status of the Sinners will be saved. If you do, the allies will be dead but Ryōshū will not have the buffs. Only the Spiderweb Entangled in Red gift in the Mirror Dungeon changes this. Also, note that each use of Ryōshū's Slay the Heavens - Tiansha [天殺] lowers Offense Level and raises Base Power (3 Offense level = 1 Clash Power on Attack Skills when clashing against other Attack Skills or Clashable Defense Skills, plus some negligible damage differences. 4 Base Power in exchange is very worth it).

[Meursault] The Thumb East Capo IIII focuses on activating his EGO Passives first, like that of Crushbound Past and Regret (and the rest). After, spend as many Tigermark Rounds as quickly as you can without getting him staggered and switching to Savage Tigermark Rounds too early, so that he maximises his future Shin (心) - Tiantui Star [天退星] and Overheat statuses. After switching rounds, you can make use of his Clashable Counter to conserve his Savage Tigermark Rounds if you want to save them for Savage Tigerslayer's Perfected Flurry of Blades [超絕猛虎殺擊亂斬].

[Heathcliff] The House of Spiders: The Thumb Apprentice focuses on inflicting as much The Duel Escalates as possible, so that he can use Sezionatura di Cervo and get Maturing Textbook more quickly.
If against a single boss enemy, clash them as much as possible (this inflicts 3 The Duel Escalates per turn if [Rodion] The House of Spiders: The Thumb Nursefather attacks the same enemy and makes Heathcliff do a follow up attack) and don't use Il Cacciatore against them unless they have 5 The Duel Escalates. Be mindful of you only being able to inflict Severed Tendon if the enemy has 3+ sum of The Duel Escalates on them + Maturing Textbook on Heathcliff.
If against multiple enemies, be careful with follow up attacks and try your best to first inflict The Duel Escalates on them, and only then killing them with Heathcliff Base Skills specifically (not EGOs).
When you have the opportunity, use Asymmetrical Inertia as early as possible to inflict Fragile with Tremor Bursts afterwards.

[Rodion] The House of Spiders: The Thumb Nursefather focuses on clashing and getting attacked by either lost clashes, unopposed attacks and unbreakable coins in order to quickly drop her Eye of Precognition stacks and enter Eye of Precognition - Overheat in order to get her Disposal skill. Always make sure to use Disposal on the enemy marked with Game Target to maximize the damage and get an opportunity to use the skill again next turn if it kills them.
She can also help [Heathcliff] The House of Spiders: The Thumb Apprentice inflict his statuses with her activating his follow up attacks.
Use her Into the Sunset for healing and the damage passive, Effervescent Corrosion for Tremor Count infliction (if you think it's worth it), Pursuance for powerful healing and Indicant's Trial for healing and spreading Burn Count in multiple enemy encounters.

Both [Heathcliff] The House of Spiders: The Thumb Apprentice and [Rodion] The House of Spiders: The Thumb Nursefather will transfer damage done to [Ryōshū] Blade of the House of Spiders, so make sure to keep them healed with EGO.

[Gregor] Dawn Office Rep focuses on stacking his Light of Daybreak status, protecting allies and making use of his self-Burn to heal himself. Use his Clashable Counter as frequently as possible along with leaving an ally (that's not using a defense skill) open for an unopposed attack, this way Gregor will get 10 Light of Daybreak per turn because of his Assist Defense. Use either Dawnsplitter or Guardian at 30 stacks of Light of Daybreak to get Crack of Dawn and heal Gregor depending on his current Burn on self.
If you need, use Dawnsplitter early to buff all Burn-inflicting allies with the Dawnherald status. Usually it's more worth it to wait, though.

[Faust] Dawn Office Fixer works similarly, but she usually gains enough Fire Butterfly Coffin with her usual Base Skill rotation. When at 30 Fire Butterfly Coffin, either use her Eject skill to get Eject - High Noon, or use her Clashable Counter to get Dismemberment at High Noon if you need to heal or want to get more Battle Instinct.
If you have a healing EGO on her, use it whenever you need, especially if it's Command : Meltdown.

[Sinclair] Dawn Office Fixer benefits immensely from his Dawn Office allies. First, win a couple clashes and enter Volatile Passion state. Use Harmony to stabilize SP, or deal a bunch of damage if he's ramped up, if you have it. Next, you can use Cavernous Wailing if you wish for him to be more tanky (he rarely needs it), or activate Impending Day to get more EGO resource afterwards, but otherwise simply have him mow down the enemies, use Fierce Charge to generate Gloom, and use Blazing Strike whenever Scorchfield accumulation reaches 100 to maximize the damage.

I cleared Refraction Railway 6 with this team in 74 turns, though I wasn't as attentive as I could be.
Hope this guide has some use and I didn't say too many obvious things :)