Full run of both Palace of Paupers areas cleared using fully craftable equipment, i.e. only the fixed properties of materials and synth items, and in particular no relic-only properties. The main takeaway here is that even under these conditions, we can pretty easily do 100k+ damage in a single W-Draw (24:37) to skip Ancient Furry King's second phase. The actual run is pretty scuffed.
Everything except the Demon Crucible and Knowledge Book is crafted during assignment 9 and I never visit the Unexplored Ruins. There's no particular reason not to make the final weapon upgrades (and there's definitely no reason for Logy to have his third-tier weapon, that's just a mistake), I just didn't want to do the plot after loading from before I took the level uncap research because I thought I needed to be under level 80 to turn on Lineage of Kings (which is like, one of three things that actually increase item damage), which I don't think is actually true after all.
Cost Bonus is Property Enhance x Property Enhance+. This doesn't seem to actually be written down in the game, I can only assume because they ran out of space in the Japanese text box, but you really can just combine into it.
Escha:
Sky Alchemy Staff [Saving Skill, Speed Surge, Beast Slayer]
Combat Shirt [Enhance Body, Boost all stats, Speed Surge]
Magic Stone [Saving Skill, Ability Power, Speed Surge]
Royal Crest [Quick Action, Lineage of Kings, (Dragon Slayer), Champ Possession; Ability Power, Boost all stats, Speed Surge]
Demon Crucible [Instant Action; Demon's Crucible, Slag Wave, Sonic Throw]
Dragon's Secret [Blessing of God, All Stats Up S; Cost Bonus, Property Enhance+, Perpetual Motion]
Dream Book [Critical Throw, Daydream; Cost Bonus, Property Enhance+, Slag Wave]
Elixir [(Recover KO S2), Ailments Down M, HP/MP Recovery S, (HP Regen S); 20-50% Automatic, Slag Wave, Perpetual Motion]
Poly Poison [Cost Bonus, Property Enhance+, Perpetual Motion]
Knowledge Book [Resonant Damage, Unstable Damage, MP Consume M; Cost Bonus, Property Enhance+, Perpetual Motion]
Demon Eye [Slag Wave, Cost Bonus, Sonic Throw]
Eye-Opener [Crit Rate Up S, Evasion Up S, Crit Power Up M; Cost Bonus, Slag Wave, Perpetual Motion]
Time Watch [Auto Revive M, Move Time Cut S, MP Consume L; Earth Armor, Sonic Throw, Slag Wave]
Logy:
Black Wing Veil [Saving Skill, Speed Surge, Beast Slayer]
Combat Shirt
Magic Stone
Royal Crest
Command Chime [Command Chime, Sonic Throw, Slag Wave]
Slag Essence [Sonic Throw, Slag Wave, Calming Effect]
Demon Eye
Dragon's Secret
Lava Cube [Cost Bonus, Property Enhance+, Slag Wave]
Elixir
Poly Poison
Dimension Bomb [4D Damage, MP Consume M, Stops Movement; Cost Bonus, Property Enhance+, Perpetual Motion]
Demon Eye
Eye-Opener
Time Watch
Micie:
Cross Rapier [Comet Attack, Fatal Attack, Verdant Gold]
Combat Shirt
Brother Call [Boost all stats, Ability Power, Attack Surge]
Soul Binder [Chains of Dest, Coop Up, Slag Slayer, Draw out Wits; Saving Skill, Ability Power, Beast Slayer]
Linca:
Slaying Blade [Saving Skill, Time Spirit, Attack Surge]
Ebony Plate [Boost all stats, Enhance Body, Speed Surge]
Brother Call
Soul Binder
Katla:
Mystery Stick [Comet Attack, Fatal Attack, Verdant Gold]
Combat Shirt
Glorious Note [Saving Skill, Ability Power, Attack Surge]
Soul Binder
Awin:
Soul Breaker [Saving Skill, Time Spirit, Attack Surge]
Ebony Plate [Boost all stats, Enhance Body, Speed Surge]
Brother Call
Soul Binder
As a bonus, I'm like 80% sure this equipment loadout can be crafted under "one instance of each item" conditions, though I didn't actually do this and routing it out is left as an exercise for the reader (notably, Cup of Life and probably Purifying Liquid have to be delayed to carry Slag Wave and Sonic Move from Slag Essence).
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