They make those big bore lever guns in shorter barrels because it doesn't take a bullet long to stabilize if it's only moving at 1800fps and incredibly fat. I love my short barreled .44 mag Marlin 1894 rancher, fast handling, and pretty hard hitting with the handloads I've packed in it.

As far as your choice, I'd go with the .45-70 just for personal preference and tradition (family thing), but you'll HAVE to roll your own, the factory ammo available isn't worth much since it's really loaded down to keep those guys that still shoot the old weak trapdoor rifles from blowing up their rifles.

That said, the .444 is showing A LOT of promise, and will probably phase out the .45-70 in time (thicker case walls with lighter bullets=fast and powerful, and in the same gun). I've heard, although never measured one, that it's only a .44 mag case plus an inch, so your bullet diameter really isn't a .44", it's a .429" (right? manuals aren't handy at the moment), so it's not really that close to the .45-70 in bullet shape/weight, but close enough, and with the added velocity, deer won't tell the difference.

My vote will stay with the .45-70, just because I love it, but it's your call to make.

Screw the 10 ring, keep them in the zero!!!