A 200gr. Sierra or 220gr. Hornady might work OK on deer if close - ie: 100yards. The Hornady is the tough bullet here and worked really well on moose when driven at only 1,940fps, way below my .375 Winchester's top-end of 2,200fps.

A .38/55 with .375" groove diameter barrel can easily drive either of these bullets at 1,950fps in the Martini, I'd expect - at around or maybe less than 40,000psi.

Make a great little pig/deer rifle, Sarg.