The clock now runs consistently for weeks at a time. Its speed is consistent to about 15 seconds per day (under 2 minutes per week). This is better than I had expected to achieve when I started the project.
I still see the occasional sudden change in speed, from running stably at one speed to stably running at a new speed. This happens irregularly, maybe once a month, so pretty clearly something physical is going on.
I know that changing the size of the gap between the inductor and the magnet on the top of the bendulum even slightly will visibly change the amplitude of the bendulum's swing. And I'm pretty sure that changing the amplitude will change the bendulum's period slightly, just as it does with a pendulum. So, it looks like the thing to do next is to look for a change in amplitude when I next spot a sudden change in the clock's speed.