"Do you know what problems I'd be facing if I linked the database to a brand new updated Moodle installation?"
If I knew the answer to that question I could make a lot of $$$$$! In a nutshell, no. Not sure anyone, who is not really familiar with your set up could tell you with any confidence.
Problems with Moodle are basically one of two things ... code or DB. So what I am about to suggest one would have to think on before trying and by all means *BACKUP* before any path taken.
Sites that have been upgraded from earlier versions through the ranks of versions sometimes develop issues that are DB related. Each step probably should have had inspected the DB schema and cleaned up the DB, etc. Most folks, however, don't do that. So it's hard to say if that's the issue or not - but suspect it might be a factor.
Anyway to run a clone of the 'problem site' on a 'sandbox' server? - copy of DB, copy of code, and copy of data directory in a box that has same if not similar environment. If so, I'd recommend using fresh code for the 2.2.x version installed via git (using edited config.php file for sandbox( pointed to a copy of the database (freshly imported) and using a copy of the data directory.
Have come to the conclusion that cron on 2 is more important than it used to be with 1.9. Any cron job errors?
As far as errors shown ... never seen such ... but a clue might be the word 'filter'. Think following that path might lead to something!