Your 7mm rem mag will do everything you want to do. No need to get another rifle unless you just want one. Moose are large animals and require a good quality bullet but are not known as being hard to bring down. I have killed several alaskan moose and they are not extremely hard to take down for their size. A 7 rem mag with a good quality bullet is plenty.
That being said I always favor the larger calibers for that slight edge I may get in some situations. I am color blind and need a lot of blood on the ground. Smaller caliber wounds many times get coverd over with thick hide and leave no blood trail. Big, heavy large caliber bullets are more effective on game. When I first got started many years ago I studied and calculated ballistics continuously. The 7mm looks good on paper and I shot the 7mm-300 wby and 7mm wby mags a lot back then. But as my big game experience grew watching numerous hits and seeing the results I began realizing caliber plays a big role. For instance the charts say the 7mm has just as much or more power at a certain range but the animals reaction says no way. Their are glitches in those charts when it comes to actually bringing an animal down. Last year on here a guy produced all kind of ballistic data on the 7mm rem mag vs the 338 win mag. His charts and they were correct showed that the 7mm hit with more power at long range and should be the best choice on elk which was the subject. They are essentially the same case just necked to different calibers. But I can tell you from much personal experience there is no comparison to a 338 win mag hitting large game vs a 7mm rem mag. The power shown by the reaction effect on the animal when hit by the 338 win mag far overcomes the effect of one getting hit with a 7mm rem mag. Although the charts don't show this.
So, back to your question. Personally I had rather hunt with the larger caliber 300 wsm
. But your 7mm rem mag will do everything you listed and I wouldn't pay the extra money if I had a 7mm rem mag in my rack. Just like everybody said. It all just comes down to personal prefference. If I were going moose hunting today and both were on the shelf I would take the 300 wsm with a 200 grain bullet over the 7mm rem mag.