Since I'm apparently the lowest DPS BLM in this thread, I went back and redid my parser (FFXIVAPP). Same stipulations: about 5 minutes of doing single target DPS, no potions, food, party member buffs, no inflating my DPS by ending on Flare or double Flare, waiting a bit until after two sets of Convert + Raging Strikes so I'm not ending on a particularly high note.
Total Overall Damage: 87,679
DPS: 264
Accuracy: 100%
Damage Crit Percent: 12.80%
Gear:
Relic+1
HQ Vanya Hat with CHC and mostly accuracy
HQ Vanya Robe with almost all CHC + 1 Savage Might III
HQ Vanya Sash with Piety IV, CHC, and ACC (last slot will be filled later)
DL gloves and pants
AF2 boots
DL accessories + AF2 ring
I don't think I could stretch this higher without good proc luck. I even have a few pieces of Piety materia (in slots where I can add no more DET or CHC) to ensure I can always Thunder II immediately after going into UI3 after a Swiftcast Thunder III.
Edit: clarified Thunder II after Thunder III.