Your scope weighs well over 1lb. You can trim that down considerably on any big game gun by using a lighter, lower powered scope. I have 2 custom barrels for my Encore, one is a 16 1/4" .250 Savage, the other a 20" .350 Rem Mag. Both are heavy taper barrels but they feel light and easy to carry in the hand. The weight is balanced between the hands when you shoot and the muzzle doesn't go "whippy" on me.
I say pick your caliber, get the barrel, have it cut short, research your scope choice well, and it will definitely be light enough to carry all day. Sean