My understanding,
BJH65, is that a "bespoke" rifle is built to the customer's specifications.
For example, some decades ago I had Griffin & Howe build for me a .340 Wby on a BRNO ZKK 602 action (
these were the dry days when original Mauser Magnum actions were quasi impossible to find and before Mauser resumed production of the magnum 98), 26" medium weight barrel with barrel band front & rear sights and front swivel post; quarter rib; Bastogne walnut stock to my measured dimensions; Suhl claw mounts; classic red rubber recoil pad; linseed hand-rubbed finish; etc. etc.
Limited production rifles such as Heym, Mauser, Rigby, Dakota, etc. do not really meet the definition of "bespoke".
All of that to say that you seem to be looking for a high quality rifle, but not necessarily a "bespoke" rifle.
In that vein, I would share that my own evolution has been to actually sell my bespoke and other limited production rifles (e.g. Dumoulin, Mauser, Heym, Mannlicher Luxus, etc.), and even my Krieghoff double .470, not so much for financial reasons but for lack of use reason, after I replaced them all with a Blaser R8.
Beside the convenience of the R8 to bring 3 scoped calibers to Africa in an airline-compliant gun case <62" linear and <50 lbs., which is necessary if you diversify your hunting to include in the same trip DG and MG (mountain game) in the Karoo, Ethiopia, Uganda, etc., I find tremendous value in the fact that you always shoot the same rifle, from home or urban shooting range practice in .22 LR, all the way to (in my case) .458 Lott, through .375 H&H, .300 Wby, .257 Wby, not to mention .223 Rem for 300 yard practice.
"Beware of the one-rifle man, he probably knows how to use it" is definitely grounded in reality, and as good as the .375 H&H is, it is lacking in stopping power for DG, and in range for PG and MG, and the reality is that we never shoot our DG calibers enough. You will likely never become a 2 MOA shooter from the sticks with a .375 H&H (you simply will not shoot it often enough), but the .22 LR barrel of the R8 will make you one with regular practice, and this will translate seamlessly to all other R8 barrels/calibers.
My recommendation would be to think long and hard about a R8, because beside being as well made and as reliable as the best of small production rifles, it will provide multiple advantages over a sole .375 H&H rifle. Besides, you can spread the financial impact over years as you can add barrels when financially convenient, without killing your Safari budget if you plan a little bit.
To each our own, but I find it interesting that most folks who buy a R8 seem in great majority to never, or very rarely, take their other rifles to Africa, even when they own many truly magnificent "African" rifles.
Just food for thought
