Today, I'd start with 70% capacity to the neck, of TB, with any bullet. I'd be inclined to try a 300gr. or heavier cast, just because. I friend left me with a whack of 310gr. FN's and in my .375/06 AH, they run an inch at 50 yards, shot to the post of the duplex retical and gave 1,385fps - plenty as a hunting load for NA ungulates.
I suspect a full case, that is 100% to the bottom of the seated bullet, might beat 1,400fps in the H&H case. Note, they are go-pow loads - no recoil and low noise. Sound like a larger bore .22 RF.