You've put a lot of thought into this, and there aren't many bad options here.
Short term, here's the action plan before you worry about changing your business model:
You need a new cleaner.
If you can't find one overnight (and I fully appreciate that you can't) you can at least start looking now and I would look for more than one. We have a "team" of cleaners, and we gain and lose a few every quarter basically. We have never had to "fire" any, the cream rises to the top and the ones who aren't that into it slowly drift away. In doing things that way you'll also discover your best cleaners are people looking for a little extra money (students, moms or dads looking to boost the household income or pay for a vacation).
We use apps "Properly" and "TurnoverBnb"
The app schedules cleanings automatically based on bookings. You'll create a custom checklist and inventory for the property to make it very clear what you want done. This will also include the cleaner matching photo examples of how you need things to look as well as sending photo examples to the app (the app requires the photo before they can mark the job done). Properly actually offers a paid service for someone to do a quality check, but I have done a review from the back of a taxi in another continent; so believe me when I tell you it makes managing these things remotely very doable.
With the inventory, the cleaners do a count after each cleaning, and when the threshold gets below what you've set as your "warning" you'll be notified of that (so you can prepare to stock up after the upcoming stay).
If you have a "pool" of potential cleaners you can start to see who is going above and beyond and push them to become your primary cleaner. The best ones often have 2 or 3 other clients, so if they're busy the day you need a cleaning they just decline (no pressure) and the job gets sent out on a first come first serve basis to the rest of your cleaners.
If you're honest and fair with your team, this system works pretty great and the best part is it's VERY scaleable if you end up really happy with the results and looking to invest in more long-distance STRs.
In my example, there would be a separate manager who actually buys/delivers supplies and fixes things. This could be you if the rental is within a weekend drive and you don't mind checking in once a month or so (might also be worth looking and minimum night stays to decrease turnover). But could also be one of your primary cleaners (for bonus pay) or another person (student maybe) to whom you pay a monthly fee for occasional stop-ins or even pay "per visit as required." If you hire full time they'll likely want % of earnings, but that's still manageable if they're doing a great job and making money for you. When I was a student I did some cleanings, and when the inventory was low the owners just sent a list to their friend who would do a bi-weekly visit.
The issue you're running into is THE primary issue that STR owners run into, and if you'd prefer to hire an STR manager there are likely one or two in your area who would be happy to take this on. I have faith that you can figure this out though and not have to spend a disproportionate amount of time on it.
If you go the route of medium-term rentals you'll want to do some homework to get connected with insurance companies and other groups that relocate folks for months at a time. If you make the right connections this can be a great option. The sweet spot for MTR was the last two years, I think we're going to see a bit of a slowdown now..but it's still not a bad option by any means (especially if you can max out those Football and Grad weekend bookings)
Long-term rentals will always be the more passive option. So if you prefer to sit back a little more, that's the way to go. No shame in it. I love STRs, but sometimes they just aren't the right fit for what we're doing.
Piece of mind has a price tag, and many owners find it's higher than the money you'll make running around trying to put out the same fires over and over again. Any time there's a chance to make a "quick and easy" dollar I remember the 3 days it cost me to clean up the mess lol.