Getting back to the core of the issue, if all is well, then opening the filler cap shouldn't stall the engine. I can only be sure that you understand the PCV to be perfectly serviceable. If you pop the clip off the PCV, this disc will come out and beneath that there should be a diaphragm (check for cracks or holes as they age), a spring and another little device that looks like a pin welded to a disc. The PCV body should have a hole in the center with a little spring-loaded disc on its underside. Check that it opens and shuts with a push of a small pen or similar.
The PCV will draw air through the manifold when the car is idling. The vented cap and a little blow-by allow it to do so. It will close once the butterflies are opened until cruise is reached (This is why the PCV is blocked by the mechanic when tuning the engine, as not all the air is drawn from the carburetor/s and will throw out their tuning tests).
But this small amount of air allowed in when pulling the cap will demonstrate the relative tuning of your engine, much like lifting the carb damper piston 1/8th" does. Opening the cap allows a little more air than usual at idle into the manifold. This will lean the inlet fuel-air ratio a little. If it speeds up, then the mixture is on the slightly rich side of a stoichiometric mixture. If it slows down, it is on the slightly lean side.
So, to tune out the problem, your mixture might be a little on the lean side or the revs a little low at idle. Richen the mixture or increase the idle to compensate. If you're sure it's not one, then it will be the other.
This is my perception of the problem, and I will always defer to a day-to-day mini-specialist if they chime in.
_________________ SooperDooperMiniCooperExpertEngineering
All garage work involves equal measures of enthusiasm, ingenuity and a fair degree of irresponsibility.
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