I'd be much more concerned you're hunting with a trigger with which you have not established familiarity, as it kinda tells me there's a lot lacking for practice, and that tells me you're likely not practiced enough to tell where the bullets will actually land.

I'm not a fan of the Axis, nothing wrong with it, but not my cup of tea. Upgrading it then doesn't make a lot of sense to me.

HOWEVER, for a deer rifle, the 300win mag is a bit much, for recoil, rifle weight, and cost per shot. For far less than the cost of a new rifle, plus optic and ammunition to go with it, you could give that Axis a pretty extreme make-over. The 7-08 is runner up as what I consider the most efficient deer hunting cartridge on the market, second only to its little brother, the 243win.

There's also no guarantee the CDL or Long Range 700 will fit you any better than the Axis, so you might find yourself needing a new stock on either of those models too.

I'd upgrade what you have before I spent money on a 300wm. (Recognize, that's said with the 300wm as one of my favorite rifle cartridges).