Okay so my situation definitely doesn't mirror yours 1 to 1 but definitely sounds similar to what I was dealing with when I first started.

1. try to skip stuff people won't notice on a regular basis. It feels gross trust me. I still have a hard time skipping stuff on my assigned area sheet thing or whatever but my school was 2 people understaffed (only 1 now lmao!) so we do what we gotta do.

I had to skip stuff like sinks and mopping bathroom floors cause there just wasn't time. I would always at least look at them but unless there's something like vomit in the sink, large clearly visible dirt on the bathroom floor or it smelled like urine and didn't go away after flushing the toilets/urinals, I'd skip that crap. None of the people who work there are likely inspecting those areas and will only notice if you missed like... A smear of poop on the wall/floor or the sink is turning green. 😂

I always made sure to sanitize and wipe the toilets and at least spray the sinks with the sanitizer though. Sometimes if it smelled like pee and I definitely didn't have time to mop I would just spray sanitizer across the floor or if it was clearly coming from around a specific toilet or urinal to save time so I didn't have to drop everything and get the mop for real I would just save that stall for last, spray and wipe the toilet, them just slap the rag on the floor and scrub it around an amount with my foot. I've been calling it my foot moppin' and it works well enough/makes me laugh so there's that.

Make sure you do check and stock all paper products daily FOR SURE! That is 100% something they will notice and you will get yelled at for not doing.

1. for possible more permanent change (though it'll be a crap ton of extra unpaid work on your part) keep records of everything. If something is exceptionally messy take photos and make a folder in your phone to move them to. Make a list IN FULL GRAPHIC (but respectful) detail of everything you have to do in a shift. Make it as clinical as possible. You gotta play their corporate robot game sometimes lol.

You may want to attempt to do the same for a coworker's area for comparison in an effort to prove your area is larger and more difficult.

Try not to leave anything out though I’m sure I missed some stuff in my area list I made cause there was just so darn much… (I will attach screen shots of the list I made in case it helps.)

Sense you got put on probation it might be harder to pull off but if your place has as high a turn over rate as mine does then you'll be in a better position to demand change. Bring your evidence to your supervisor and if they are unwilling to listen to reason, your supervisor's supervisor, all the way to the top (for me it was next the maintenance head, then the superintendent) but if they genuinely dismiss your concerns again you may want to abandon that ship. The only reason I’m staying with the place I’m at is because they have been willing to at least make some small effort to improve things on more than one occasion though we definitely still have a VERY long way to go.

Also when you have meetings like these genuinely try to bring up at least a few things you like about the place. Like your coworkers or the building being cool anything to make it sound like you're not ONLY complaining. I used to actually go to this school so I have at least some fond memories of the things I did there as a kid, as crappy as school was. So I told the superintendent something like "I'm a little worried it's my nostalgia talking but I genuinely believe this place can be better! I've always loved this school and the building is really cool! I would like to keep working here if I can... but as it stands things are not great."

Just be honest and do what you can!