While I can't speak to the 336 conversion, I blew a ton of money trying to make a couple of Win.94's feed a 44 x 356BB. The solution was to convert the top ejector Post 64 action to the BB version. A new BB carrier, and both guide rails did it. My G.S. still had to influence the mag tube over towards the loading gate, to help the big nosed slugs make that turn. Those BB cases have really thick case heads, so you only get 300 Sav. capacities. Maybe its better to keep it as a 375 Win., and put a heavier 24 inch barrel into it. Something like the 38-55 Legendary Lawman series. OTOH, you could solve both problems, if you could find one of those Lawman's in 38-55 Win.
My next 44 Marsh ( 44 Marlin Short), will have one of these 24 inch, half Oct. barrels, to dampen down both the recoil, and the muzzle whip. Full magazines shoot to a different point of impact, than loading one, single shot, over a bench. I dumped off a very early 375 Win., that I bought new, for this same reason. The lighter bullets of the 7mm Shooting Times Easterner, don't seem to exhibit any of this barrel whip drama. Nor will the 38-55 Win. in those Legendary Lawman commemoratives.