I noticed that there's a folder in the install directory named "roms". Is it possible to use MAME to run the files in that directory?

This question is prompted by the lack of gamepad support in the main menus and occasional graphical issues (shadows go a bit wonky in some levels).

I tried using ShumpMAME, but the games don't appear in the MameGUI list, even when copied to shumpmame's roms directory.

Unfortunately not; all the files are different from the MAME ones. Pre-recorded music can be used instead of emulated music so so it could be that they've modified the ROMs to provide the ability to toggle the original music.

Custom MAME builds might support these versions one day but for now they're unusable.

I actually tried modifying MAME to do this, to no success.

I WAS able to make a version that runs the ROMs from dotemu's IREM pack, but I couldn't get it working for Raiden Fighters -- the ROMs in this were too different from what MAME was otherwise expecting and I couldn't figure out what it wanted.

"Pre-recorded music can be used instead of emulated music so so it could be that they've modified the ROMs to provide the ability to toggle the original music. "

This seems really likely -- Raiden Legacy apparently has the more accurate music than in MAME, so the sound being pre-recorded instead of emulated would explain this, and would also explain why a lot of the data doesn't match.