This myth about short barrels and fast powders persists!
There is no reason to go to a faster powder with a short barrel, whatever powder gives the highest velocities in a 26" barrel, will also give the highest velocities in a 22" barrel. Period.
The rifle in question just may not like heavy bullets, this could be due to many factors, the least of which is barrel length. The length of the barrel has little to do with accuracy, it's how stiff it is that counts.
Anyway, what powders have you tried?
I find Retumbo, RL25, RL22 and H1000 to work quite well with the bullet weights you list, RL19 will be a poor performer I feel, but you can only try it, I guess.
Let us know how you go.