It is definitely time for you to take up hand loading.
You are correct with regards to the factory 375 being anemic, and worst is, there was never a good reason for them to be like that.
The few firearms that were chambered for it were more than capable of much higher pressures and therefore velocities.
A properly loaded 375, from what I remember from Enforcers data, will put you in the 2000 fps range with a 220gr bullet, which will without a doubt put down even a bull moose at 150 - 175 yards.
A well placed shot will do the trick even with factory, but with a moose, I would definitely want to be 100 yards or under to be safe, even though it technically is capable of a bit more, but loading your own is still the best option.
If you want to send me some brass and bullets, I would be happy to load some moose pills for you at no charge but the return postage, primers and powder are on me.
Of course, you will have to send me a moose roast !!
Ranger