The real problem is overheating. If you are handy with a soldering iron I guess it's relatively quick and cheap.
Because the failure is due to overheating, if you are going to pull the amps and start soldering anything, you should probably go ahead and replace a bunch of things since the rest are probably near failure anyway.
The IC which is a power transistor, labeled as Q1, is manufactured by IR.
I'd replace the transistors, two of them are made by IR w/ Bose's generic part number (137110), two with IR part numbers (FIZ24).
Digikey sells these for $1 each.
http://www.digikey.com/IRF.DKS$P=IRFIZ24N-ND
I'd replace at least these caps as well: C110, C130, C16, C183, C172, C203, C31, C7, C8, C25, and C19.
Anyway it sounds like you know your way around a circuit board. If you do fix it youself, I'd love to get a nice write-up with photos for the FAQ because I'm sure there are many others who would be able to save money.