No one can really answer the question on "when they switched." They seem to have alternated back and forth for a few years. That might not be true, because they also didn't produce guns in serial number sequence. We just assume it because there is no real rhyme or reason to early guns being heavy barrel occur, just as tapered ones appear much later, seemingly after large numbers of the heavy barrel guns were out and about. All that from the unreliable serial number point of view.
Don't read too much into barrel profile. It'll just confuse you. When you hear folks preaching something about when a feature started or ended on a K22, allow your eyes to glaze over. Unless its surrounded by a lot of back pedaling (as I'm doing now) you can pretty much just disregard it all. If it makes you feel any better, the company historian is often suprised at features when he letters guns. Things he often thought were general rules sometimes aren't the way he thought they were. And he's seen more guns than all of us, probably.