@flourishdesignstudio† Okay, I was able to replicate the Warning on another site which is good, didn't want to debug on your site yet couldn't replicate.
For now, you can get rid of the warning message by turning WP_DEBUG to false. In your wp-config.php file find the line that says
and change true to false.
What you are seeing is a warning and not an error, thus turning debug to false will make it go away.
I still have to find the reason it is happening. Will keep you posted.
On Relevanssi, you just need the Expand shortcodes option checked and pages/posts checked, not the accordion post type or taxonomy because it's a private post type, not public. The page that the accordion is on will show in the search results.
If you want to explore the option of having each separate accordion show in the search results that would take some customization, probably not much but make the post type public and give a slug. That won't solve the slow search.
Not sure why your search is slow, that shouldn't be Accordions but will test on a local install and get back to you.