iPhone - free up photo space for transfer to new phone

Solution 1:

Here's what seemed to work - it's non-obvious because it seems to require waiting vast amounts of time with no indication that it's going to work.

So as I wrote in my (first) update, I disabled iCloud Photo sync. That helped a little bit, as did deleting various other random stuff, so that the phone-to-phone transfer could proceed. The new phone was still VERY unhappy because it was right up against its capacity limits, everything was super slow as it tried to perform tasks that require a little disk space elbow room.

Next, I re-enabled iCloud Photo sync on the new phone. Nothing really changed, but it started saying that it was uploading photos to iCloud (incredibly slowly). Over the course of the next couple days, it seemed to make a bit of progress uploading, until suddenly today I'm seeing a MUCH happier storage report:

I think it either made a breakthrough once it decided everything was uploaded, or it was able to free up some space by uploading things and that gradually let it free up more space by uploading, etc. etc. etc.

I hope this can help someone encountering similar issues.