Do you think one could be converted to shoot .375 Winchester and would the revolver take it?

Yes. In fact, I believe you can get a factory custom shop .375 BFR. I had a .30-30 BFR converted to .307 Winchester, to match my Winchester 94 in that caliber.

I just called the factory and got a quote for the BFR in .375 with optional octagon barrel, slimmed and rounded grip, 7.5" barrel, fluted cylinder. $3100. I could save $350 with a round barrel.

Not sure it's worth that to me for a toy pistol. Doesn't seem like a 30-30 conversion would be a big deal for a competent smith, provided there's enough meat on the cylinder and barrel. Starting with a $1000 30-30 might make more sense financially, if possible.

There is plenty of meat on the cyl and barrel, as BFRs are made in .444 and .45-70.

Seems like ~$1000 ought to be in the ballpark of boring and chambering the cylinder and fitting a new barrel.

Sounds like one heck of a fun project and revolver!