I know your using a bolt action model, but the Hornaday Flex Tip rounds (designed for lever action rifles) have good performance at 100-150 yds. According to their specs, you’d get 1225 fps and 800 ft lbs from their 160 grain Flex Tip at 100 yds with that barrel length.
I read somewhere that the hornady flex tip doesn’t feed well in the rotary magazine of the 77/44.
Ooops...my mistake. I copied the 30-30 ballistics info by mistake. Their 225g .44 would be traveling 1416 fps and have 1002 ft lbs of energy at 100 yds from a 20” barrel. The flex tip design reportedly offers more consistent expansion and bullet performance.