If you really wanted to go to year 5 and you trigger the TLSQ accidentally, and really want to finish it, you could just extend the duration using the gem hack and wait until it's fixed, although we have no idea how long it will take for JC to fix it.
Also, in my first playthrough of the game I didn't skip any TLSQ, but did move very quickly through the story of years 5 and 6. Each TLSQ has a priority for which order it will appear. The Out of Sorts quest for me didn't trigger until I was in year 7, meaning it has a very low priority to trigger.
Year 5 has a lot of romance TLSQs, and also the O.W.L.s which have a far higher priority. So long as you reach year 5 chapter 4 before Out of Sorts triggers, you will probably get the other TLSQs first (which have higher priority) which will prevent Out of Sorts from triggering for a while longer (which will hopefully be when it's fixed).