I have found a workaround for anyone running into the same issue:
1.) Disable FNEI and load your latest save after the game restarted
2.) Save your game with FNEI disabled. This reduced save file size by 2.5 Mb for me!
3.) Enable FNEI and load the purged save file.
-> FNEI search runs perfectly smooth again.
Looks like the gigantic search history was indeed causing the performance issues.
@npo6ka: maybe consider adding an option to not retain search history (or limit it's length).