A/C not cooling

One of the first things I would do would be to put a set of A/C gauges on it and test the high and low side pressures to see what the state of charge is. Those numbers would also give you an idea if it was the charge or if it's a worn compressor by the way the pressures change. Those would be the most suspect parts as the problem occurred gradually. Or to verify that the charge isn't the problem do a full recovery and re-charge by weight. It should take between 1.3 and 1.5 pounds of 134A.
https://www.2carpros.com/articles/re-charge-an-air-conditioner-system

From what you posted I suspect it is either low charge level or a worn compressor. Both would cause the same type of delayed loss of cooling.

You can usually get them at the places that do the loan a tool routine, which is sort of a gimmick anyway as most have you pay the full price of the tool, then refund the money when you return it, but it can be good if you don't think you will ever use a tool more than a couple times. Let us know what you find once you have a set on hand.

Not yet. I wouldn't do anything until you can do some testing. No reason to spend money on parts you may not need.

Okay, you have a very low charge. You should see a pressure like those in the chart with the compressor working. Static pressures should be slightly higher than the temperature when you are testing, So if it's say 75 degrees you should see a static pressure around 78 PSI. That would be with the compressor off. If it's 90 degrees it would be about 95 PSI.

It sounds like you have some leakage, now that you know the charging methods I would put some UV dye in it and then go hunting for it. You can also look for oil staining from the oil in the system. The dye makes it much easier though. Beyond that it's great to hear you have it working.

What were the pressures at when you finished? When it shuts off then starts working after setting I would look at the system pressures while running, that somewhat suggests a higher than correct charge as the system will shut off if over pressure than may start working once the pressure has equalized.

For 80 that's about 15 PSI high and could be the issue if the high pressure cut out is a bit aged. The only way to know for sure would be to run it until it shuts off and then see what the pressures are when it shuts down. Attached are the numbers the switch should operate at. The increasing numbers are where the switch cycles So on the low side the switch turns on at a pressure higher than about 25 PSI and off at about the same The high side will shut off the A/C at a pressure above about 400 PSI and as the pressure drops it turns back on between 200-250. So a weak switch could easily be turning the system off at 350 or so, and it comes back when it drops back below that. But I would check the pressures simply because running them high can easily damage the system.

I would check the pressures first, it may be that they just need to be lowered a bit to make it work properly. There is also the possibility that it was working too well and iced up the evaporator core, that would trigger the temperature sensor on the core to shut it off until it thawed out. I'm leaning more toward the pressure switch but want you to know the other items that could act that way.