Well, I had an essay written here, but then I accidentally hit the back button. So this version should be shorter.
I plan to replace the GFCI with one of those from the link above as that seems the simplest thing to do at this point, although I'm not sure about brands but I think they should be about the same. I also plan to recheck all the exposed connections that the GC touched when he disconnected the 5 outlets.
I also wanted to make clear that the washing machine trips at the same 2 points in every cycle, and it doesn't matter what cycle is used or if the heater is on. It also doesn't trip when water is added to the cycle at other points, like the permanent press spray during spin. And once you reset it, it works just fine until the next fill is over, and always right at the end.
Additionally, the only thing downstream of the bad GFCI is the washing machine and an unused plain outlet on the "load" connection, as my GFCI three-light tester trips that outlet when I press the button in that outlet.
As to who did what, the GC disconnected the 5 outlets, everything else "old" was not touched by anyone since renovations started. The licensed electrician did everything else electrical, including adding the subpanel, adding the new work breaker, and moving the old work one. My spouse was here during the inspection, without the electrician, and the inspector made the GC tell the electrician to change the breaker for the "new" work to an "AB" breaker (as in the initialism, it is also marked with an "AB" and a test button). All the other breakers are regular ones, as far as I can tell. FWIW, the inspector did not take the cover off the panel, according to my spouse, so whatever that implies about the inspector / contractor / electrician. Maybe that means it wasn't a "final" inspection, if there is such a thing?
Finally, I think we're getting close to the point where if a new GFCI doesn't fix this problem, then we will talk to the city inspection office. We may not be able to force the issue, but the inspector might. But that might also be a long shot, so I've debated getting the washing machine out and seeing if there is anything obviously wrong with it, like a leak or loose wire or corrosion.