Yeah, I figured it might not be easy to fix (since we're running these games in a way they're not meant to be run in.) However, I did get a workaround for this problem, using batch routines.
I noticed the "starting" logo pops up, then goes away. After a couple seconds, the game loads. On other games (like normal MAME), the "Starting" notification stays up until the game takes over. So somehow, control is passing back to Mala for a bit before the Taito X game loads. So that's why the reorder layout screen option doesn't work. The layout is reordered before the game even runs.
Using a batch routine, a screen pops up and has a "press any key to continue" before passing control back to Mala. If the game is run before closing the batch routine, and "reorder layout" is on, the layout will reorder upon closing the batch routine window. Not the smoothest looking option, but it works.
::Launcher for BlazeBlue Contiuum Shift
::BBCS.bat
@echo off
echo.
echo Launching BlazeBlue Continuum Shift
D:
cd\taito\BBCS\
typex_loader.exe game.exe
echo.
echo.
echo Don't press any joysticks or buttons until the game loads.
echo After you quit the game, pressing any button to return
echo to the Mala Frontend.
pause
Of course, this means you can't have the window minimized or hidden for this "emulator" in Mala.