Alright, I’ve “fixed” my problem–by re-installing. I decided to experiment by installing a fresh version of 2.3 into a subdirectory and then upgrading that. Everything worked perfectly so I made a WP-Export of my real blog (having already backed up my modified theme files) and then deleted it, re-installed it, applied the upgrade, and finally installed my custom-theme afterward and imported the blog. Short of re-applying my settings (permalinks and all that jazz) and making new widgets (I had copied them out of the page-source), everything was perfect.
Thank you very much haochi and MichaelH for your very patient and helpful suggestions, and I hope scitec and BlocoDaBarra are able to fix their issues as well.