Second rewound coil, better result
This second try has 2000 and 4900 turns, and it gives a reasonable 4.5uA unloaded. I'm going to try 2000/6000, hoping for a higher resistance than normal on the drive coil, in turn hoping that causes lower amplitude and lower current draw.
If so, that will work better with modern silver oxide cells, which have a higher voltage than the mercury cells these watches were designed for, 1.55 vs 1.35 volts. This isn't usually a problem but does plague some particular 214s.
It would be nice if I could fix that too, while I'm at it!