I think the stories about SB actions being softer steel are urban legend. No personal experience with them, but I've never seen documentation of a failure from inferior metallurgy. Posters on other forums have checked rockwell hardness and they seem to check out.
I think the limiting factor here is the action design is from 1898 and intended to be used with rounds in the 7x57 pressure range. Sure, they've fit bigger rounds in them safely, but if I were building high-pressure magnum from the ground up, I'd pick something else.
Primary reason not to build the rifle in the OP's cartridge choices are that the action is too small for the cartridges. the 1898 action being designed around a cartridge with max length of 3.230" or so with a mag box length of 3.310". The .338 WM and other "short magnums" can be easily fitted to the actions with minimal effort. Opening the action to accommodate cartridges that exceed 3.400" in length is much more involved and, in the mind of some, a questionable practice.
With regards to metallurgy and heat treatment, I often gear that the actions were soft yet have never seen evidence of such. I think many confuse these actions with the Spanish made military actions. In fact, the SB commercial actions were sometimes found to be too hard as early heat treatment consisted of flame hardening in much the same manner as early 1903 Springfields. As a result some suffered from the same malady of being to hard/brittle. this condition most often exhibited in receivers with a purple hue.
