to install seimitsu LS-32-01 properly, there's no way around it, you have to disassemble the stick a little bit, don't worry, it's all common sense and should be easy., just unscrew the bottom metal plate of the stick, that way, you can remove the microswitch pcb temporarily and you have more room to screw the mounting plate on to the bracket.
for madcatz stick brackets there's two ways to do it using the Seimitsu SS plate. you can either use two screws, mounting it using the middle holes TOP and BOTTOM of the mounting bracket... or four corners of the LEFT and RIDE parts of the mounting bracket. get me so far?
here's an image to help you, as to the extent of the joystick dissambly.
http://legendius.web.fc2.com/my_documents/madcats_sf4_360_snap/madcats_sf4_360_9.jpg
that's the one for the left and right mounting points... imo its the better way to mount LS-32's in madcatz sticks...
but seeing that one of your screws were damaged, you can make use of the middle holes on the top and bottom wing of the bracket, as pictured... if you feel like the screw is stripping... its not actually the screw, its the metal plate itself, the other unused holes aren't fully threaded, so you're making the threads as you screw something in it for the first time.
after you're done just safely put back the pcb and gates, make sure the 5pins are facing away from the buttons.,
granted that pic was for an SE stick, but it should be the same for TE sticks.