Don't be afraid to neck size only. The general wisdom is it only works in bolt actions, but it's all I do in my Savage 219 so it oughta work in that H&R.
I have two loads in Hornet; squirrel load A is a NOE 45 grain WFN design, plain based and two grains of Bullseye. Squirrel load B is the Lee Bator (Midsouth sold it a while back, the current Lee is a copy of the RCBS bullet, not the Bator), cast very soft, gas checked and using 6 grains of 2400. That one is a bit more meat destructive, but my Stevens 322 won't feed the NOE bullet so that's where the Bator comes in.
If I need a .22 centerfire for more than that, I'll grab one of my .223s.