Engine overheats when A/C is on

There are a number of reasons this could happen. Clearly what you have covered would be the first and foremost of concern. However, since you addressed them the next items are actually part of the A/C system. We need to start with checking the pressures of the system. This may point to the issue or give us a better idea where to go next.

What happens most of the time with the compressor is it is actually locking up and adds that additional load to the engine and it causes it to overheat.

Here is a guide that will help with this but let's start with what the pressures are in the system and then evac and recharge it just to make sure it is properly charged. Then retest the system.

https://www.2carpros.com/articles/re-charge-an-air-conditioner-system