I don't know if the 44 mag dies will work easily. I never tried that, but depending on what company made them you may get by that way.
You will probably have to de-cap by hand before you try them because the “guts” of the decapper will have to be removed in most cases to clear the extra .940 of brass length.
Lee dies are fairly inexpensive so if there is any problem you will be able to get a set and not break the bank.
I did a lot of load work back in the 90s on the 444 Marlin. I found the 320 grain gas checked LBT bullet to be superb, but many of the Marlin rifles needed to have the cartridge lifters modified to feed them. It was a simple modification, but necessary about 50% of the time.
The only down side to the 444 is the fact that Marlin used a 1-38” twist for them. It seems as if that would not be fast enough to stabilize a 320 grain bullet, but it did in the rifles I tested. The big advantage the 458 has over the 444 is the fact that it can shoot much heavier bullets and also it can be had with barrels twisted 1-14” right out of the box.
In the case of you wanting to do a full blown custom job on a Marlin 444, or a converted Mosin Nagant or LEE, McGowen makes correct barrels with perfect rifling for such work. Their 444 barrel has a .422 bore with .429 grooves and can be had with a 1-24 twist which is the cats meow for the 320 grain bullets