Well, my problem with my LB75B TLB got fixed today. I've been putting off working on this solenoid clutch circuit since mid-July. In the meantime, I've lost over 50 lb and the problems with my legs have almost completely disappeared. Today, I went back to troubleshooting and found the problem. It was a dirty fuse socket. Previously, I had a blown fuse. I put in a new fuse and it didn't fix the problem. Today, I removed and re-installed the fuse. Like magic, the solenoid clutch started working. The fuse was new and clean, so the fuse socket must have been a bit dirty. I used the tractor all afternoon and it's working perfectly.

EDIT: On the polarity reversal that had me so confused. When the relay is removed there appears to be -12 vdc, but my digital meter has very high input resistance and with a tiny amount of current leakage, this could just represent contact resistance or something similar. With the fuse socket clean and working normally, the polarities are correct.