Howdy,
When I look at the factory performance numbers of the 38-55 I see numbers that any handgun hunter would drool over. A 255-grain bullet at 1300fps is a 100-yard deer cartridge by any standard. My dad killed his first whitetail with one in the 1940's. His dad traded the Marlin for a Winchester 30-30 the next season and that was how Dad developed a low opinion of Model 94's. The Marlin was truly a superior rifle and the 38-55 is a great cartridge.
It will never be a .375 Winchester, either, but you can bump the velocity up a bit. I would recommend cast bullets sized to .001" over groove diameter. For some reason the .38-55 bores don't have a standard groove. Modern Winchesters are generally .375" while modern Marlins run as big as .380". I size my Lyman bullets to .379" and they work fine in my Winchester and a buddy's Marlin. I'd recommend slugging your bore to find out what you have.
Lucky kid!
Bitterroot Bob