If the belt is loose, it will feel loose. If it doesn't feel loose, meaning there is no movement of the tensioner arm when you pull on the belt, then consider the belt tight enough and move on.

Your pressure readings are virtually the same every time it trips out.

It would be interesting to have a voltmeter on the low pressure cutout switch and see if the voltage there trips when the clutch quits or if the voltage remains when the clutch trips. This would tell you if the CCU is giving up its signal or if the Klima relay is tripping. If the voltage remains after clutch cutout, then the CCU is still asking for compressor and the Klima relay or circuit is the culprit. If that is the case, an ice cube relay in place of the Klima should fix you up.

If OTOH the voltage at the low pressure switch goes away at clutch cutout, then the problem is in the CCU system, very possibly a temp sensor or temp sensor circuit.