A valve can't misfire - but it can cause one. My guess is that your actual diagnostic code is P0302 which is a cylinder 2 misfire. Can you confirm that? Cylinder misfires are most often caused by problems with spark (such as caused by your #5 ignition coil) or fuel delivery. Mechanic engine problems can also cause them due to lack of compression.
Can you find out how the mechanic knows that you dropped a valve seat? Or is it just a guess? Was a compression test done?
If you did actually drop a valve seat, I'm going to say that you might be better off finding a salvage yard engine. A dropped valve seat has a way of immediately producing lots of other damage including to pistons & block. Or if it did drop a valve seat and damaged nothing else, this does not mean that you need a new head. You take the head off and send it to a machine shop for rebuilding. In this case there is no "back order."