I don't know how TEs and SEs are set up, but my HRAP3 has a little switch that changes the stick between buttons (dpad) and axes (the left/right analog sticks) - setting it as the left analog stick works for 2DFM2nd games, whereas the buttons don't.
If you don't have such an option, then unfortunately you're going to have to either get another stick that does, or use a silly hack solution such as Joy2Key to translate your stick movement to keyboard keys for movement (warning - may induce input lag).
On a somewhat unrelated note, I probably should play this game more often, but my HRAP3's wire is kinda fucked up and I need to fix it.
TEs have that same switch that switch it from LS>DP>RS you need to make sure it's set to LS for it to work.