It's possible that this particular GFCI is a little more sensitive
than it should be, and swapping it with a different one may cure the
problem.

Switching both the hot and the neutral through a double-pole switch is
almost certain to fix it.

Well, it was worth a try, but the DPST switch did not fix the problem
either. It worked fine for about two weeks, then tripped again a couple of
days ago.

As always, it trips when the fan switch is turned "OFF", not while it is
running.

I've tried two different GFCI's, and three different switches, and they all
have the same results.

I'm baffled. The wiring is new and in good condition. The only two things I
can think are the fan itself is bad, or condensation is draining back into
the fan and causing problems.

Still, it seems like the DPST switch would completely isolate the fan from
the GFCI. There shouldn't be any current flow even if there was a problem
with the fan. And there have been absolutely no problems while it is
running. Only when it is turned off.

Other than rewiring to take the fan off the GFCI, or replacing the fan, are
there any other things I could try?

Anthony