I bought a .44 mag off my stepdad a few years ago. I have reloaded two loads so far. One is 240 grain Speer Lead SWC with 6.75 grains of Unique powder (Unique load) and the other was 240 grain Speer JHP with 23 grains of H110 powder (H110 load) Both loads work great... except the Unique load feels for like a .22 than a .44 Mag

and the H110 load kicks like a mule and I can't hit the broad side of a barn from the inside with it.

Is there a happy medium here that anyone knows about? Using the H110 is awesome to shoot because it sounds awesome and kicks hard... but not very practical. Eventually I'd like to take it hunting in handgun only areas, but right now I know I am not accurate enough with the .44 mag to do this. Any ideas?
Thanks in advance!
Dustin