Buy quality brass like Norma or RWS, neck size only after initial firing & you should have at least 10 firing per case easy! You will have to watch the case length as it will stretch due to its rather tapering case; take a note of your smallest length case in your batch after first firing & keep that length as a reference - trim to suit.
There should be tons of reload data on the web for the .375H&H, even the reduced loads side of things.
Hopefully you'll get someone to chime in for those.
What powders & projectiles are you thinking of using?