OK, you can shoot 44 magnum and 44 special in the .444 Marlin. I did it quite a bit when I had one. They will not feed from the magazine however, at least on the Marlin. I have never had a Win.94 in .444. The cases come out fine, no bulges, cracks etc. The .444 is just a lengthened 44 magnum, which is just a lengthened 44 special.
I have shot 2 1/2" 410 shotshells from a couple of 1895 45-70 Marlins, a 1895 ss and a 1895 LTD1. I used Win. shotshells and they worked fine, Rem. occasionally split a little but still extracted fine. They will not feed from the magazine. I tried some in my 1895 barrel chambered in .450 Alaskan, they stick in the chamber badly.
If you can find them 410 2" shells also work the best, especially if you have a 45-70 with no throat, like the 1886 replica's.