I have a 2000 and not that problem.
Just to remove any doubt, I'd install a voltmeter and check voltage (may be at lighter plug) when this happens. A/C clutch current is not that much and should not cause a severe voltage drop but there have been a lot of voltage problems, bad grounds, with this model and I just wonder if it could be a factor here; a higher RPM might run the alternator to a higher voltage and clear the problem....this is just speculation but clearing it out leaves the way for other options.