The 44Mag has a 1:38" twist rate which wouldn't be ideal for a .444M rechamber specially if you want to shoot bullets heavier than 270gr, but the original Marlin .444 had that twist rate and worked, later was changed to 1:20" tho. The biggest problem with the .44mag Handi is the oversized bores, they can be hard to get to shoot accurately even as a .44, what going to happen with a lot more powder, it may be an expensive conversion if it doesn't work, although several have done home rechambers to .445 Supermag and had great results, so the extra powder may be all that's needed to get good accuracy out of the oversized bores by obturation of the bullets to fill the bore.
Your PM concerning the muzzleloading .44mag rifle may be in reference to the original H&R Shikari which had a ramrod under the barrel, I don't know if the frames are up to shooting the .444M round unless you kept them loaded down to .44mag velocitiies and pressure. It was also available in .45-70, but limited to trapdoor loads which are 28kpsi and below, the .444M has a SAAMI MAP of 44kcup. The Shikari bores had much nicer rifling that the newer rifles and were excellent cast bullet shooters from those that have posted about them. Hopefully some of those folks will offer their opinions on the subject.
Tim
http://www.chuckhawks.com/444Marlin.htm