If .44 Mag and max of 7.5" barrel is the only option then I'll take a Ruger Redhawk Hunter (KRH-44R)
Ruger Redhawk Double-Action Revolver Model 5003
If you prefer single action then make it a Ruger Super Blackhawk Hunter (standard or Bisley)
Add a scope later.
If .44 Mag is not the only option then I'll take a 14" Encore in .35 Remington or 7-30 Waters - with a scope.
That said, I have an affinity toward the .45 Colt and my *actual* hunting handgun is a 9.5" Ruger Super Redhawk in .454 Casull.
Since you have the Encore frame already.................