Since the 22 Hornet is a rimmed cartridge, doesn't it headspace on the rim rather than on the shoulder?

Either way, if your 'smith sets the barrel back a full turn and cuts a new chamber, either regular or K, your headspace problem goes away. K seems the logical way to go on a non-collectible Hornet.

My Savage Hornet experience is limited to a 19H, a couple of boogered-up 23Ds, and a couple of 340/342s. None had triggers worth writing home about and only the 19H remains to gather dust.