Grenadier:
You are right to advise caution with shotgun conversions, but the sheer number of these things in common use today with no safety issues whatsoever, my own .577 Light Nitro included, might prove your overall assumption incorrect.

Regarding your comparison of 11,500 psi vs 42,000 psi: the basal area of the Marlin case is only a fraction of the basal area of the 12-bore shotshell, so the back-thrust on the action is probably in the same ball-park. With the much thicker chamber-walls of the .444 on a 12-bore action, no worries about barrel strength.

Having said that, the BP load suggested in beleg2's post is a little high and would not be something any of us would recommend for a vintage rifle.