Perfect, thank you!
I may have actually found something. The actual search query is exactly the same on both versions, I just compared, so luckily there is no massive search query problem, it is something with the arguments only.
It is still very hard to track, but there is a possible problem of passing the search fields to the query, when using the regular vs. the index table engine – basically always the regular engine parameters were used in some cases.
I made a patched version, and I am uploading it with this reply. Please install this one, clear all layers of cache and test again. I am not a 100% sure you will get the same exact results as in the previous version, but there should be a difference.