130 grain TSX/TTSXs and 150 grainers work fine on deer. Ins a 300 WM if you won't be shooting beyond 400 yards I'd go with the 130s. If you will be working beyond 400 I'd go with 165/168s. The better BC will will be useful once you get that far out.

Varget and the 130s is a great choice. Varget is still good with the 150s. Were I to go with the 168s I'd start trying out RL17/RL22.

I get stellar accuracy out of the 130s in my 300. 150s are just as good. I wouldn't hesitate a second to use 130s on elk or moose. I would not expect to stop one in an elk or moose either, at least not unless you try to shoot one end to end or corner to corner. Even at that I wouldn't bet on it staying in the beast.