Thanks John. I already bought the replacement GE relay, but if that turns out not to be the problem I'm sure someone here will have a need for one at some point.
The thing that concerns me is that when the fridge was trying to kick in, the muffled buzzing sound didn't seem to be coming from the relay. It sounded more like it was coming from the back corner behind the condenser fan.
If the compressor is shot, I won't pursue a replacement. It's a nice fridge, but I prefer a bottom freezer type. If it were a BF model, frost-free or frost-y, I'd be more inclined to pursue a new compressor.
The compressor did jiggle a bit during attempts to cycle on, as if it wasn't totally frozen up and dead, but I know that doesn't necessarily mean it's OK, either.
The sad truth is that even if the compressor is fine, the access issues to replace the wiring between the fan and the relay could be what really ends up rendering the fridge a lost cause, at least as far as my ability to repair it goes. If anyone has replaced a condenser fan or related wiring on one of these, I'd appreciate any helpful information on how to get at it. As you can see in my reply (ending in 356) above, the opening is small and I don't think I can even fit my hand through it to reach the fan, and I certainly have no view of the mounting screws.