I really appreciate the replies from everyone. It's nice to see that
some folks share my interest for navigation.

I've placed a bid on a taffrail log on ebay. If it gets eaten by a
shark, I suppose I could whittle up another rotator and then rate it
for error. That seems better than the alternative, which is not having
a run distance. I rarely use ebay, so I'd forgotten to check there for
compasses. Thanks for reminding me. There are plenty of good options
there. I think I can find the kind of compass I'm looking for on
there, or, failing that, I'll take Steve's advice and swing a handheld
compass for the spot on the boat where I will normally be using it.

Some of the yacht "navigation" practices I've read about in blogs are
indeed appalling. The most shocking example that comes to mind was the
entry of an unfamiliar atoll from below decks, using an electronic
chart (CMAP, I think it was called) plugged into a GPS, along with the
remote control for the autopilot.

Regards,
-Maxime