2,400fps with a 300gr. Hornady would be perfect, I'd think. Any faster and this thin jacketed RN might over expand.
In Rod. H's tests, the 300gr. Interbond (gold bullet) showed even more expansion than the standard RN, with a typical bubble-gum-stick-together huge final diameter-type expansion. We also tried cup-pointing some of them and the expansion was greater yet, even lower initial speeds.

I suspect if you take a normal 300gr. RN, and file the nose off flat with the top of the jacket or cup-point it slightly with a drill bit (won't take much) you'd see more rapid expansion from your .375 Flanged - yet not alter the accuracy or penetration much, as you'll only be removing perhaps 10gr. of lead.

The size of an exit hole does not always indicate the amount of damage done internally, but is dependent on the expansion, of course, and most importantly, it's velocity and the leading shock wave at exit. A slower moving, expanded and expended bullet that barely makes it through the hide, will make a smaller exit hole than a faster moving bullet, it seems.

If one cuts an animal apart and sees little internal hemorrhage or tissue damage when the lungs should have been well holed (2" to 3"?) or shredded, then one might complain the bullets did not expand well.

Norma's "Alaskan" brand bullets have thinner jackets for expansion at lower speeds.