Old thread I know, but I did get this working on my machine in case you were still having problems, Clickhea.
After some time, I ended up getting around to installing SSFIV:AE with two U360s (all buttons are using an I-PAC, and not the U360s built-in encoder). I had some troubles similar to what you described where I would try to buzz in with the second player and I would lose control, or where I would press 1up's start, and then it would think a second player was joining and then I wouldn't be able to control player 1 anymore.
All problems now seem to be resolved after installing Joy2Key and using only the keyboard 1 & keyboard 2 configurations in the game, making sure that joystick 1 & joystick 2 settings were cleared and set to <NONE>. Everything works perfect now.