LS56/LS58 is easy, I've put one in a Hori Fighting Stick PS (the variant with the metal top plate) and from what I've seen of both sticks they can be treated the same. You remove the metal plate, remove the joystick inside, (EDIT: Dremel off the 4 posts that held the original joystick), keep the shaft and balltop (maybe spring too, been a while), shave the actuator so it's the same height as the old one, remove LS56 mounting plate, use mounting plate as template and mark holes, drill holes in Hori, screw stick in, tweak holes if one of them is off, put Hori back together, and wire stick in.