Umm, errr, . . . umm, I have seen many Marlin lever action 1894s, in .357 magnum, new out of the box, that will shoot one inch groups all day long from the bench, with factory ammo, so long as you have a very good 4 power scope (think Leupold), and steel mounts. The most accurate factory ammo was the cheap PMC soft points, 154 grain. But, I don't think PMC makes it any more.
I am not exaggerating with this reply. I think many people who are experienced with the 1894 Marlin will tell you exactly the same thing.
And, if you want to spend a little more money, and hand load, I have personally seen a friend with an 1894 Cowboy model, with the 24 inch octagonal barrel, plus well tuned .357 handloads, consistently shoot a 1/4 inch group at 50 yards from the bench.
So, you really don't have to build a custom rifle for what you are looking for. Most used 1894 Marlins, in VG+ condition, can be had for about $400.
I don't know how the .44 mags would shoot.
Best,
Mannyrock
Mannyrock