RemFarmer,
There are few rifle actions chambered in 357Mag that won't tolerate the MAX chambering. The longer case lets you use slower powders to generate equal pressures, over a longer period. This means you can shoot equal-weight bullets faster, or heavier bullets at like speeds. This takes you from a marginal deer cartridge to one that has a little more room for error. It also lets you shoot heavier bullets with the knock-down power needed for the heavier targets.
I would suggest that you speak with David White of D&T Gunsmithing. He will give you an authoritative answer on whether or not your action is up to the task and there is not a better man out there for doing the chamber reaming.