Also Elwood Epps gunstore in Ontario. Yes, that Elwood Epps, now sold as the lod man passed away some time ago. I was referred to them from Canwest when asking about a
45-70 conversion similar to the discontinued Gibbs Rifle: NRVO ULTIMATE LEE ENFIELD, http://www.chuckhawks.com/gibbs_summit.htm
They will fit a new barrel, modify the receiver/extracator, supply & mount a dovetail ramp foresight, and turn the barrel to fit your stock, all for about $500
Ellwood Epps Sporting Goods
E-mail: info@ellwoodepps.com
Website: Ellwood Epps Sporting Goods
A magazine is another matter. I found & bought a new Japaneseicon made 6-round single-stack 45-40 mag made for them, at Old Western Scrounger, for $75. VERY few left.
Old Western Scrounger The Old Western Scrounger LLC.

For .375, I think it would be possible to modify the Lee lips, as the casing diameter & shape are not all that different from .303. Certainly less so than the 45-70.
I very likely will do so with a (poorly) sporterized No 4 that I now have, that I was considering parting out.

Good luck, and let me know how it comes out, if you do it.