Could be the compressor clutch itself. Some compressor clutches are not replacable without overhalling it. Most of the time you got to buy a whole new compressor, not sure exactly how it is on the Wrangler, have not analyzed mine yet.
But one way to test is to hotwire the compressor clutch fire, put a temp switch on it and click it on, this eliminates everything else. If the clutch fails to engage, its definetely the clutch and needs to be replaced.
If the clutch does engage and no issues at idle (when testing it) and never disengages until you flip the temp switch, then we got to start looking elsewhere. Such as making sure the pressure switch is working, when pressure is too low, there is a switch that tells the controller not to engage the clutch, you mentioned pressures are fine (hopefully you adjusted your reading for ambient temps) so could be the switch itself. You could always hotwire the switch to also test to see if that is a cause as well (after the clutch test passes).
Basically gotta run down the line to start testing the AC components.