A '94 should be able to handle it. Have both a '94 carbine and a Trapper chambered for the .44 Mag.
Use a Speer 4457 240 JSP, but might have to find another as this one appears to be obsolete. 24.0-24.3 grains of H110 (using auto disk w/1.54CC) COL 1.600 +/- .010 (can tighten this up if I want, but would have to be anal about fired shell lengths due to the cannelure on the 4457 not being right where I want them). This formula comes out of my Trapper (16" barrel) @ 1720 fps average over 1000 rounds. Out of the carbine with the 20" barrel the average is 1810 fps.
Totally agree with the lead...1200-1350 fps max. In fact with 240 LSWC my load is 9.0 grains of Unique and I get leading, even though they barely average 1200 fps. A little bit better luck with 270 Grain Ranch Dog mold w/GC. These run about 275 grains lubed and with Hornady gas checks, but can not get more than 1310-1325 FPS before they start to show signs of lead. So I load them with 9.5 grains of Unique...then they just bump 1300 fps.
Buddies 1894 Marlin chambered for the .44Mag doesn't lead at the throat and I can push them both the SWC and the RD GC's a bit more...but the 1-38 twist makes them unstable and inconsistent when trying to get more than 50 to 100 yards out of them. The Winchesters clover leaf when clamped in a shooting vise.
The Winchester has a short, tight throat and that is where the leading shows up...nothing further than the throat. My Trapper has a 1-26 twist and my Carbine-Black Shadow) has a 1-20 twist.