First, you are not talking about a "rechambering" you are talking about a "rebarrel". Rechambering is where you leave the bore size the same and ream the chamber of that barrel out to a different caliber, for instance rechambering from a 300 win mag to a 300 RUM, both with bore size of .308".
Rebarreling is putting a barrel with a different bore size on your existing action. For instance your case of putting a 300 win mag barrel on your existing 7 mag action.
But to your question, both the 7 mag or the 300 win mag will do essentially the same time job on Whitetail and Elk. With Moose the 30 caliber would be a definite advantage because of heavier bullets and a larger frontal area. That being said, I'm sure there are a lot of Moose that have been taken cleanly with the 7 mag. Just use the appropriate premium bullet and even work up some loads with the 175 gr bullets and you should be good to go.
The real reason you should be thinking about "rebarreling" is to have a semi-custom rifle
with a name brand aftermarket barrel put together by a gunsmith who makes his living off his reputation. In all likelihood it will give you better accuracy and a sense of pride that you made the decisions on the rifle and have something special. It does for me.