First case of this to be reported. Have you tried running a frame limiter and locking FPS to 60?
I already had Riva Tuner set to limit framerate to 60, since it's my monitors refresh rate. I ran MSI (and Riva Tuner) just to see what my fps was since it was going so weird. Solid 60 fps in battle, even with the delay (the animations are smooth though). Even when I disable the animations mod, still solid 60 fps when it's going super speed (not sure why it's running at 60 with it disabled, maybe that has something to do with it?)
Also, when you post load order, use what's given from the Profile Details button in 7H.
Oh wow didn't even see that button lol, I'll update the OP.
EDIT: Forgot to mention, I'm running both ff7 and 7th heaven in compatibility mode for xp sp3 as it keeps freezing at black screen if I don't.
EDIT2: Game runs super speed even when starting it directly from the exe without any mods. Not sure if it's related to the delay though. Steam version of the game runs normal though.