Can anyone recommend a refrigerator that is REALLY quiet? Or, possibly, one that has a pleasant, constant, noise profile instead of the "100% quiet for hours... then suddenly an insane BRANGGG sound when the compressor kicks in"? Do these even exist? It shouldn't be huge, so all 2-door versions are right out. I could maybe even go for a mini fridge.

propane and natural gas units are nearly silent.
or go the commercial route and put all the noise/heat making equipment on the roof or out back and pipe in the cold/hot exchange lines to the separate kitchen unit.

Wow, I've never even heard of propane/natural gas powered refrigerators. Need to look into that. Probably not a good choice for me in an apartment building though? Also I can't put the cooling element outside for the same reason.

As for the Sun Frost fridges... Don't think I could get those here but I don't know why they would be any better than any other refrigerator either?

From what I've read, super-insulated -> needs less cooling ->they use a smaller/quieter compressor. Sort of analogous to SPCR silent PC philosophy.