No, I've not dug into the main panel yet.
But, remember...
Even though the outlets in the bathrooms are dead, the GFCI in the basement is still working. That's why I think the GFCI is the culprit, something in the inner workings.
I disagree.
Go to Homeless Depot and just buy a $10 outlet tester, with a GFI test button. Plug it into the outlet in question. If everything is working, you'll see two amber lights. Push the button and the GFI should trip.
I'm betting you won't see two amber lights. I'm betting you'll see an open neutral. The power comes to your bathroom through the GFI, but the neutral doesn't return to the panel through the GFI. You have an open neutral.
Question: Are the wires to the dead outlets under the screws, or are they pushed into the little holes in the back? If they're pushed into the holes, cut 'em off, strip about 3/4" of wire, and attach to the screws. See if that helps. Often, those push-in terminals compress the wire and lose tension over the years, leaving a loose (and very unsafe) connection.
Remember the color coding:
White to bright
Black to brass
Clean to green