I am a little confused. You say the car DOES NOT have a Klima relay. Is that because it has never had one, or it has been removed? According to the wiring diagrams your car should have a "compressor cutout control unit" that could be called a Klima relay. It appears to be separate from any other relays.
I believe you when you say this is not a pressure problem because I saw the picture of the gauges. However if there is no compressor cutout control unit (Kilma) then it doesn't have any bearing on your problem.
Could you give any information on any alterations done to the A/C system. Not parts changed, only changes made to the way it was made.

Thanks,

PaulM

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84 500 SEL (307,xxx miles)