/wp-admin/admin-ajax.php Error 500

I have a single Wordpress 4.9.16 website that is throwing Error 500s when taking many actions in the admin interface. When I try to do things like add a new category, nothing happens in the front end and my web inspector shows the error.

I have tried:

• Renaming my .htaccess file and letting WP rebuild a new one
• Increasing Wordpress memory limit
• Increasing PHP memory limit
• Disabling all plugins
• Re-uploading core files in wp-admin and wp-includes

And after taking each of those steps, I still experience an admin-ajax error 500 when trying to add a category.

My next steps are to either

• Change my theme
• Update to 5.6 current release.

I have a few questions, but basically it all comes down to how to fix my admin-ajax 500 error.

1. If I change my theme to something out of the box (one of the Twenty ______ themes), and then change my theme back to my current theme (a child of Spacious Free), am I likely to experience big problems? Or will most/all of the configurations remain?
2. Is it likely that I will be able to update to 5.6 if I'm receiving this error? It feels like this is a logical step in diagnosing the issue. I've been holding off because I haven't had a chance to test the site in 5.x, though.
3. What else should I be looking for?

Thanks. -Ben