Many thanks to all who posted. I stopped by my usual independent, who worked on my venerable 420SEL for the last 3 years. He lifted the hood and inspected, listened to it with A/C on, off, then on again, and pronounced the dread sentence. "Yeah, compressor's going."

It may not be so bad; he thinks the evaporator and other parts are OK. I'll call him a little later to get a price on the compressor and labor, and schedule it for next week. (He said the A/C should be OK to use sparingly until then, and I'll be parking the car at the airport while I'm out of town this weekend, so it'll be easy enough to do without A/C.)

Three good things, though:
1) This was the original compressor, with 7 years of hard work fighting NO heat. Not too shabby!
2) I'll have him change the cabin filter while he's at it. This may also solve the problem I posted about earlier, the odd vibration from the far side of the dash -- which I realized yesterday does not happen when the A/C is off. He can take a look up under there while he's doing the filter and see if anything is loose or worn. Maybe the vibrations from the ailing compressor are being reflected up the ductwork to the air vent, which seems to be where the annoying noise is coming from.
3) I'm philosophical about it. After all, the rule of thumb is that you should prepare to spend about 10% of the purchase price of a used car in repairs during the first 6 mos. So far I'm on budget!

__________________
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-- Paul W. (The Benzadmiral)
('03 Buick Park Avenue, charcoal/cream)
Formerly:
'97 C230, smoke silver/parchment; '86 420SEL, anthracite/light grey; '84 280CE (W123), dark blue/palomino