Muzzle of the Lee-Speed .375 is .655"dia

I don't know what the minimum outside dia would be for your rebore project.
You need to call a barrel maker, and/or get references for someone to do the rebore. They will be able to tell you minimum wall thickness for your barrel at muzzle, but I bet you'll be just fine!

I think weight and balance will be the biggest factors.

Cheers
Tinker