Thank you!
So, after hours of researching stackoverflow forums, the ACF help forums and other github resources, I managed to find a solution. Seems like, the bypass solution we had was not working, simply some fields were still missing. I have added few additional lines of code, which is now a combined solution of 3 redundant methods, to make sure all of the ACF fields are parsed one way or another. I wish they had a simple function, so many developers have problems with this same exact requirement.
Anyways, please keep a copy of the wp-content/plugins/ajax-search-pro/ folder on your server, as some of the search plugin files were changed (in case you reinstall). I will however include this solution in the upcoming release, so you don’t have to worry about that anymore.