Smallbore,
Sounds like a great project and if you can come in at the proposed $25K, should be viable.
As for your questions,
The 470 is an obvious choice, but I can see the dilemma regarding the 375.
On one hand, the flanged cartridge is the classic, "proper" choice, but lack of factory available ammunition may cool some prospective buyers' enthusiasm. Although on the vintage market I have noticed that the geniune .375 flanged magnums do command respectable prices right there with the over .40s.
I do feel that the 9.3X74R is becoming quite popular here in the US and for all purposes a close competitor to the 375 in all respects but price. That is where the 9.3 would gain much appeal as far as cost and availability of ammunition and reloading components.
As for the market gap, there are some doubles in this range, but not many, and especially not in the English style.
Would they be proofed in London and then sold in the US?