I just did a bit of forum research, and apparently this has happened to a lot of people. I guess I was lucky for the problem to occur this late (or not, considering that the warranty would have covered earlier).
SOME threads here suggest that firmware reinstallation might solve the problem, and I actually don't think I ever updated to 1.14, so that's worth the try.
Class A, I suppose you are right that service would still be the cheapest solution. I was a bit worried that I might be charged for the off-warranty service while not having the problem fixed, in case they were unable to replicate the problem, but given that it is a known problem, that might not be an issue. BUT if I buy a K-5ii, I will gain these benefits: a) not having to be without my camera for weeks; b) getting a second camera, so I can have one with my 300mm mounted and one (slightly unstable) with my 16-50mm on field trips, and c) better AF for my bird shots.
Yes, I know, I'm trying trying to rationalize spending money... but there's no FREE solution anyway, so I might as well make the most of it!