The .357 Maximum was originally developed for use in the Hangun Metallic Silhouette game.
While I don't have the exact figures in front of me right now, I have serious doubts that the action of a Winchester M '92/clone or Marlin 94 would be long enough to function with the additional 0.400" OAL of the Maximum cartridge. I'd do some serious research before buying a LA .357 Mag. carbine to try a conversion, although OAL wouldn't likely be an issue with a Marlin 336 or Winchester 1894 action. It wouldn't be cheap, and would be of questionable practicality given the cartridges these carbines already come chambered for, but it could be done.
You might want to check the hunting regulations before you spend your money. While the cartidge itself is certainly capable of taking deer at 100 yds or less, it may not meet the current requirements for minimum bullet diameter and/or weight.
Unless you're a handloader, or willing to become one, I'd recommend choosing another round personally. Factory ammo for the .357 Maximum is essentially nonexistant, although cases are still available from Remington.
In something with the weight of the NEF single shot the added recoil of a .44 Mag or the like wouldn't be much of a Big Deal, and certainly it would be much easier to feed. As a practical matter, I don't think you'd be losing much in the way of range (especially now that Hornady is making LEVERevolution ammo in that caliber. The published data for a 20" bbl with the 225 gr. .44 lists MV as 1870 f/s, and ME 1747 ft.-lbs. At 100 yds. it's 1429 f/s and 1020 ft.-lbs.. With a 100 yd. zero, it's only dropped 5.5" at 150 yds., although energy is down to a semi-marginal 787 ft.-lbs. at that range.