Mr. boxlock could just get the quick & dirty answer as to suitability of grandpa's Stevens by contacting Aaron Little thru his FaceBook. https://www.facebook.com/amlittlebespokegunmaker/

My personal take? Bushed firing pins would be the lipstick on a pig, the action is not suitable for containing "Nitro" (.375 H&H belted) pressures. That "antique" (excuse me, vintage) action is not quite equipped with double underlugs, 3rd bite, and steel intended for the pressure.
Shotgun ~8,000-10,000 psi modern rifle ~ 40,000-55,000 psi

- Mike