Copy iCloud Photos library to a clean install
I ended up following ankii's suggestion and just chancing it by turning iCloud Photos back on and letting it upload 100,000+ photos.

On the plus side, it did sync successfully without duplicating any photos.

On the minus side, I started it on 09/08 and it just now finished on 09/17. So that's 9 solid days of "uploading". It was on a mostly idle iMac with broadband and it didn't seem to be taxing either the CPU or the network, so I'm not sure why it went so very very slowly.

My total data usage for the time is less than half the size of the library, so it does appear to have saved some data. No way to tell how long it would have taken to download the library from scratch.

I still feel like there should be a better way, but I can report that copying the library to the new system and turning on iCloud Photos does work.