I'll spare you the gory details and the pea-soup graemlin because the whole thing is now fixed, thanks to the generous help I received on this board.
The problem was in the connection between the Dec cable and the RJ45 plug on the Dec motor housing. This connection experiences twisting forces as the RA axis turns. The Cat 5 Dec cable, being cylindrical and stiff, resists the torsion enough that the wire contacts inside the RJ45 plug become intermittent.
A whole boatload of seemingly random problems ensue. The thing starts behaving like a demon. (I swear I had a girlfriend in college like that - sweet & innocent one moment, and hurling lightning bolts the next...)
I suspected bad cables from the beginning, but after going through a pile of cables from different sources I couldn't be sure - the problems persisted. What solved it was David Pavlich's link to a site that sells flat cables. The flat cables flex with the movement of the RA axis, and keep their contact better. Thanks, guys!
And check out this Saturn from two nights ago!