I've done things as simple as opening the top of the drive and it started working again. This isn't a long-term fix, but it seems to confirm that the drive was just a little tweaked. I'm guessing that the freezer trick has a similar effect of shifting things, just a little.
Replacing a circuit board is pretty far out as I bet each drive has an individual defect map, so it would likely have random problems after. I've seen this done, with success, but I wouldn't bother.
If it matters a lot, get somebody professional to help. If you can live with total loss, I'd sure pop the top again... just long enough to transfer the data.