If the .38/55 factory ammo would chamber without being to tight on the necks, it would shoot just fine.

The size difference, possibly raising pressures due to the moderate to fast burning powder used in the case, would be outweighed due to the very low pressures the ctg. is loaded to - afterall, factory ammo is still loaded, in the States, to BP ballistics, ie: about 1,320fps with a 255gr. bullet. Measuring a factory 255gr.might be interesting. Quite possibly, they could be only .376" in which case, no contest - no difference for the gun to recognize?

I'd make it true .375" groove diameter and probably regulate it to use the most excellent 225gr. Hornady SP and 235gr Speer. The 220gr. Flat point Hornady that worked so well on moose for me, would also be a contender for all-round bullet.

Of course a nice 255gr. FP & HP cast would also be a good bullet to regulated for, for everything.

Many options in that calibre. Increasing the size to .377" would be a mistake, I think, although .375" bullets would still shoot well, I'm sure. .004" undersized bullets shoot very well in my 9.3x57.