Mine is a 35 Remington w/o the muzzle brake so I can't answer about how effective they are. The recoil on my gun is, is, kinda hard to describe, it doesn't hurt or sting like a 454 DA revolver, but the muzzle will flip up 90% when shooting of a bench and bags. Not much rearward push. The way the gun balances, a little weight to muzzle, almost neutral balance.
You won't want to shoot 44 mag in a 444, the base and rim of the 444 is larger than the 44, you might get one to fire but the case would rupture and vent gas thru the action.
Competitor Corp is making the latest version of the Lone Eagle so if you want a new and improved gun they are availble, of note, the Competitor Corp gun parts are not interchangable with the lone eagle, so says Comp Corp.
http://www.competitor-pistol.com/