GFCI Circuit Curiosity

What happens if you move just one of them to the other bus?

And I assume they always remain on the same two circuits? I can't imagine what could account for that behavior, where which hot the GFCI is on matters. What's on those two circuits? Not that it should really mater. These are the only two GFCI breakers?

Although I can't rationalize this to your problem, the catch all for strange problems affecting differences between the two ungrounded conductors is to be sure the neutral connections are good going back to the utility. Do you measure exactly the same from neutral to each ungrounded conductor when the panel is energized?

Just for clarity...

In this case, when you say "each ungrounded conductor" do you mean the hot wire at every breaker or just the main hots coming into the panel, i.e. each of the 2 busses?

In other words, how exactly would you suggest the measurements be taken?

Yes, the test should be made between the neutral bus and each "hot" (AKA ungrounded conductor) . Ideal is a reading exactly the same but if it is within a volt or so it is probably OK. Any difference reflects voltage drop in the neutral.

It eventually trips.

Yes.

On the bath circuit, just a WaterPik. On the kitchen circuit, there is a toaster plugged in (but I've tested without the toaster plugged in, and the results are the same).

Yes, although I'm thinking of adding another for the Kitchen Garbage Disposer Circuit.

After battling a couple of GFCI circuit ocasionally over a few years, I discovered something interesting. If I put both GFCI breakers on one buses, they both stay on. If I put both on the other bus, they both pop randomly after anywhere from a few minutes to a few months.

I'd be interested to hear any insights anyone here might have on this.