+1 on the Hawk bullets.
The 375 Win is a reloading cartridge. Straight walls are easy. When I had mine Re7 was the best powder.
Brass can still be had and even 50 will last a long time.
Like so many here, I lean towards oddball stuff and just figure on reloading. Currently bullets seem to be the hardest to acquire.
I am down to my last box of Hornady for my 348 Win so Hawk will be my next choice.