Battery trick - Perhaps there's an off chance that is a simple RAM issue. :/
Try a different SD card with fresh install of the game. If you're using an older Class 4 or 6 rated card, maybe it's too slow.
After trying the above two, restore the SysNAND with the image made from step 1. This concludes that the original state of the 3DS firmware is intact.
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I'm not sure if your bug is fixable. Yours seems to be the first documented case. This GBA VC issue appears superficially related to this specific DS(i) issue where the touchscreen input is broken.
I don't have the right tool at hand to open the back of the 2ds, so can't do the battery trick right now. Will have to try that later. Trying a different SD card tomorrow as well.
No faulty or broken part on the o2DS. Everything works perfect.
I just find it so strange it only happens with the FireRed games and its romhacks. Pokemon Emerald and previous titles run just fine.