"Raiden to Leviathan?" and "New Battlefield?"

If I switch the sprite pointer to Terrato, then all 3 of those bugs go away immediately.

Yes this sounds a bell. While doing monster expansion, I found one code piece per espers but having as ID their monster / sprite ID (384 + esper ID) in upper $C2 which is a continuation of bank $C1. I had to change all of them to prevent buggy esper call since I was expanding monsters number by 128. There are a few $C1 call for each piece of code and I believe it's something GFX related for the least. Leet Sketcher has a good upper $C2 disassembly but sadly bank $C1 is almost not commented. Here are the places where there is a "LDX monster / sprite ID" for all espers. This could maybe lead to a solution if you isolate and understand Terrato functions calls.

Code:

org $C2EB52
org $C2EB69
org $C2EBC2
org $C2EBE1
org $C2EBEE
org $C2EC01
org $C2EC1C
org $C2EC29
org $C2EC36
org $C2F020
org $C2F073
org $C2F08E
org $C2F0C1
org $C2F0E2
org $C2F0F9
org $C2F109
org $C2F119
org $C2F129
org $C2F14D
org $C2F16B
org $C2F195
org $C2F203
org $C2F211
org $C2F221
org $C2F231
org $C2F24D
org $C2F27B
org $C2F289

Edit: I could probably spend some time on this to verify my theory and since you're not (yet) an ASM guy. I have a school project due next week and an exam but next weekend I should probably be able to allow myself an hour or two on this.