I'm having a similar problem, sans arcade cab.
With Joy2Key or Xpadder, my FightStick TE (360) will work fine for TH06-09. But with 10 onwards, it is impossible to play. For 10, 11, and maybe 12, the game keeps "thinking" that I'm continously pressing up, and with SWR, when I go to set up my stick, and I'm configuring up/down/left/right, I'm fine, but as soon as I attempt to map the first non-directional button, the game detects that I'm using a controller and auto-remaps directions to pad U/D/L/R. So as a result, when I try to start a round, I have to use the keyboard to make menu selections as the game is having issues with my controller, and on getting into a round I can move around via my stick (since stick presses are being registered as key presses by the game) but I can't attackk (since they're registered as game controller button presses).
I've read about XBCD, and that is out of the question as it has issues regarding the FSTE being made by MadCatz.
So is my stick pretty much obsolete with newer games?