It's possible that the problem is with your CD32 and not the SX-1. We have two CD32s here, one of them works fine with the SX32 and the other doesn't work with it at all. When I opened them both up, I noticed that the one that won't work with the SX32 (but still works on its own) has a big capacitor expanding and ready to explode. Old capacitors and batteries are common causes of many problems in old Amigas, so maybe you could unscrew the CD32 and check it out.
I'm going to be sending the CD32s off to get all their capacitors replaced (along with some A1200s and A2000s) soon, so I'll report back if this fixes the problem with the SX32 not working with the CD32.
Oh, and the SX32 is similar to the SX-1, it's just an internal model and fits better. They both work the same.