Intermittent AC - out of ideas

[upallnight]

Best way to determine the problem is to connect a set of gauges to the system. From that you can tell us what is the high side pressure, low side pressure and the ambient temperature these readings were taken. Anything else is just a guess. A good AC shop should be able to perform this if you don't have the gauges or lack the knowledge. You can command the th compressor to engage. If the pressures are not according to the pressure chart for the ambient temp that you have you found the problem. With a variable compressor even if the clutch is engaged it may not be pumping the refrigerant as intended.