The model 7 is a little bit smaller than the 700 short action , it could be made to work with a WSM case but youwould be limited to how far you can seat your bullets out , seeing how the Wyatt's mag box is the same for the 700 SA as the M-7 I don't see why you would be anymore limited than anybody building a WSM on the SA 700. That said , I would suggest rebarreling your M-7 to 300 WSM , get a little longer and a little heavier barrel , maybe a 28" #5 conture from say Broughton , Bartlein or anybody else that make sa 5R rifled barrel , the barrel land profile is a personal preferance of mine , it does lend to a little higher velocities.
Your factory stock would work but for the cost of having the work done to it to accept the bigger barrel and a good bedding job you would be better served with a new stock.
Alright lets recap with money figured in
#1 New barrel , $300 any top brand
#2 action blueprinted , Wyatt's box installed and barrel installed , $400
#3 New stock , $500 any top brand
so for your $1200 you could have a very well built gun in a caliber able to shoot to 1000yds on deer and probably 600yds on elk comfortably. Now you could sell the BAR and that would be a big down payment on a great scope , either Nightforce or Leupold MK-4 , or my new favorite Nikon Tactical.
Seeing how its gonna take at least 10 weeks to get a barrel made probably double that if you get a McMillan stock , which I'll never buy another one of. So if you ordered your stuff now you could get it to a smith by early spring and he could probably have it to you by mid summer and that would give you a little time to get some load work done and a little practice at longer range. I'd probably choose a 300WSM or 7mmWSM for the caliber choice
The time frames and dollar amounts are pretty modest and the cost could be cut several ways as well as the time frame depending on what your exact needs and wants are.