The guys at Andrews couldn't have been more helpful. A quick test of the offending beast reproduced all the weirdness that I was seeing. As soon as they heard the motors they could tell they were buggered.
Anyway, Andrews immediately gave me a new replacement mount and tested it there and then. After years of star-hopping, I was just in awe of this thing just happily doing it all by itself. There's nothing better than a Goto mount (except maybe two of them)!
So, to conclude this sombre little saga; thanks to everyone who offered help, and thanks also to Andrews, whom I couldn't recommend more highly. Their prices seem to be the lowest (at least on the stuff that I was shopping for), and their after-sales service is great (no, I'm not on commission).
