Revisiting this briefly…
Further SEOPress updates have caused further problems (both cosmetic and console errors), and (in my view) we’re now at the point where we can no longer use new versions (5.x) with ClassicPress. I will not be renewing my pro license.
I have one client CP site that is using a lot of SEOPress features (including schema, local business, etc) and for this site I have rolled back to SEOPress 188.8.131.52 and SEOPress Pro 4.7.0 (and I’ve tweaked them so they report versions of 184.108.40.206.2 and 220.127.116.11). This has resolved all the issues.
For other CP sites that use less SEOPress features, I’m migrating them over to my own ZP SEO and am now going to try and spend more time working on the ZP SEO codebase to add the other features I need (redirects, basic schema, etc). So a full-featured ZP SEO Pro, optimised for ClassicPress, may eventually appear after all (if what I develop for my own benefit produces something that is marketable).