Good call, 9.3x74R is a solid chambering and mighty practical, also quite available in doubles. I can see the attraction of a .360 double kept trim too, but would have a hard time embracing it over the .375 Winchester that essentially adds a just shy of 1/4” more powder to the same case with my preferred bullet diameter.
I was dangerously tempted to buy a factory Model 21 double rifle out of the states in .375 Win. But this project was far more sensible once I broke myself out of the spell it had on my imagination, and came to face the poorly considered risk to my savings account.
Sad day telling the excited boy hidden somewhere inside you to stuff it, for financial sensibility. Fortunately he got excited again with this, very affordable project.