Bingo

Finally, the primary part that has caused me so much woe was found...the shaft with the worm gear that drives the RA clock (okay, the one that cancels the Earth's rotation) has a piece attached to the end, secured by a set screw, with a gear which is in turn driven by an electric motor. The hole in that piece, which is placed over the aforementioned shaft, was not drilled axially to the gear teeth. Put another way, it's really crooked. As in, it looks like someone hand-drilled the bloody thing.  What those gauges are saying is that the error was over 100 thousandths of an inch, just one inch from the bearing holding the part. Cavemen used to be better machinists.

How I managed to miss it was by going over all these parts singly, when I should have been looking at groups of parts together. Granted, for a part with obvious marks from being machined all over it, I can forgive myself for thinking the inside was made the same way.

So anyway; the hole was enlarged enough for the part to fit axially, and I added three set screws to not only take up the slop but allow some adjustment later if needed.

The weather was mostly cloudy, so I didn't get to test it hard....but I was able to get some star trails five minutes long with the mount intentionally out of place, and they were straight lines. Before, they had a v-shaped jog every 110 seconds or so. I did a quick and dirty polar alignment, and got a bunch of 120 second frames with no drift. So the 30 second restriction is lifted. Of course, with my old camera, 30 seconds is the limit of what I can shoot without manually exposing each frame; and with a light-polluted sky, it's not always good to shoot longer than that. But now I have options, and I won't have to toss a third of the frames I shoot. This was the last major step in transforming this old pile into a useful photography tool. Not a great one, but good enough for me to spend a lot more time learning with.

A closing thought? How about this-in all the years I've collected little bits and sticks and clamps and cute fancy magnets so that I can get a dial gauge to sit exactly where I want it, I suppose I never actually needed it on something made entirely of aluminum and brass. I spent more time finding a way to attach the gauge then I spent fixing the part. The moral being, you should ALWAYS get that extra tool, even if you aren't sure how you'd ever use it-you never know.