Aleko
You know my feelings on a medium bore double. [I have a 9,3x74R Chapuis]. Also you know I would like to try a 375 H&H double to "test the envelope". Also EVERY double under 400 should have a scope fitted in QD mounts.
I will recommend 3 scopes for your 375 double.
Leupold 1.5x5 or the Leupold 2.5x8, I like the Heavy Duplex
in both scopes. Or the 1.5-6x 42 Swarovski with the circle dot illuminated reticle.
I have the 2.5x8 Leupold and the Swarovski in rings for my 9,3 double.