Well, I'm showing my lack of knowledge of the big body cars. I'm surprised that there is no sensor.
If the problem is in the climate control unit, heating the solder joints might be worth a try. I know it is not uncommon to fix a 124 Climate Control. This will repair a cold solder joint(not totally uncommon) and can fix a broken circuit board trace.
Also, ensure that the system is fully charged. If the high side pressure is too low, it will cut out the compressor. Since this is happening on acceleration this is not likely.