FWIW, SpaceX has launched stages after full-length (3 minute plus) burns on the test stand, on a schedule that wouldn't allow time for that kind of teardown. They'll need to do something to clean the engines out eventually, but if several minutes of operation were enough to cause serious gunking, then between those test runs and the multiple runs of the grasshopper test vehicle for landing sequences, they've seen it and know how to deal with it.
(Incidentally, SpaceX is known for keeping some aspect of their operations trade secret, rather than patenting. So, if they had some solvent that dissolved the gunk and simplified the cleanup process, or some such similar trick, it's likely that no one outside the company would know about it.)