Ok, I get that the OP doesn't reload and has his reasons for the 444 but he also seems to be asking what I think is the best lever gun cartridge .
First , best for what? I don't much hunt so for me that answer is what gives me the most fun shooting.
My Marlin 39a is a great gun and a lot of fun to shoot.
My Rossi 357 is also lots of fun and covers a lot of ground with everything from light 38spl target loads up to blow out the walls heavy bullet 357 loads.
My Marlin 44mag cowboy also covers lots of ground with all my reloads.
I also have a Marlin in 45/70 , winchesters in 30-30 and my newest find , a Marlin in 375win. This latest find would have been almost unshootable a couple of years back because ammo and brass was very hard to find and really spendy . My buddies at Starline are now kicking out 375win brass so everything is cool with this great gun.
Don't make me choose! I reload most everything I shoot and have fun with them all.
Same guy that sold me the marlin 375win tried to talk me into taking his 444. Gun was a older near minty condition gun and he was offering me a decent deal but I just don't feel the 444 like the OP does. Doesn't mean the OP is wrong for him , just not for me.