Hi!
Thank you for all the details, I have found some errors in your configuration, and I have corrected them to make I think according to your needs:
– The ordering was not set by relevance, I have changed that back to the default: https://i.imgur.com/aMrGBfB.png
– I also enabled a more strict keyword logic: https://i.imgur.com/nUJsDX6.png
– The index table was generated, but not enabled. I have enabled them for both post types as well as attachments.
– I have changed the ordering so that attachments are shown before post types: https://i.imgur.com/jOcRwKo.png
– I have removed the tablepress_table post type from the items to return, as those are not separately working post types, but embedded in posts/pages. The index table has already indexed all the embedded tables in them.
I think this is the most strict and probably the best configuration for your needs. It is still not perfect of course, but it should do the trick.