This is what's causing it:
$FF02:20 A2 10 JSR $10A2 A:08 X:38 Y:1F P:nvUBdIzC
$10A2:00 BRK
The game is JSRing to data when the dialogue box is called, however, this is indicative of a bigger problem.
See, the JSR being called here isn't a JSR at all: The 20 is actually the tail end of a STA command (8D 06 20). Tracing back and finding the JSR to the beginning of this code shows that the pointer *is* correct (When compared to the known good dump of the japanese game), it's that the data isn't where it's supposed to be in ROM.
Things are misaligned between the patched and original ROM from somewhere between $38000 and $3FFFF (The end of FF1 in the ROM). The misalignment gets more pronounced further into ROM you go.
I guess this means either the patch is corrupt or it was based on a dump of FF1&2 not found in the GoodNES set. I've applied it to all the bad and overdumped variants (With both LunarIPS and SNESTool), and even ran the game under LoopyNES (What the readme states was used for testing) and the same issue persists.