Follow-up,
Not sure exactly what fixed it, but I disassembled the whole thing (down to the PC board), carefully cleaned the optics, and put a new actuator on it.
Both now work perfectly, and they are quite amazing. You can really tell the difference in games like Robotron where you need precise movement and short throws. It almost feels like I'm cheating!
I'm a little confused by the need for dedicated ports. I have a totally modular panel and all of my joystick and button ports are mapped multiply (2 ports for joy1, 2 ports for joy2 and so on - see the web site). I just plugged in a 4 way joystick along with the P360 on the same joystick port (joy1) and both work perfectly for in-game play.
Any reason why I would need diodes if it is working fine?
Thanks again for all of your help!
Doc-