jim-y,
Just a bit more information:
Ruger makes a rifle for 375 H&H length cartridges and it is listed on their website. This is the length that you will need for either the 7STW or the 7MM RUM.
Both the RUM and the STW's have the same rim diameter of 0.532" which is a standard magnum boltface. The difference is in the body diameters where the RUM body is larger than the STW's. The magazines for the RUMS need to be wider front and rear to have them feed correctly. Remington has the mag. box with triangles cut out front and rear to allow the cartridges to "spread out" so that they don't lock each other up.
The work required to make your 7 Rem. Mag. into a 7MM RUM is the same as making any other standard length action hold and feed an H&H length case. You will need new bottom metal, probably Sunny Hill or Ted Blackburn, expensive. You have to lengthen the interior of the receiver by cutting back the feed ramp as well as moving or cutting the bolt stop back to allow for the extra length of the cartridge. The rails will have to be opened up and lots of adjusting done to assure proper feeding. The ejection port will have to be modified to allow loaded cartridges to be unloaded (remember that they are longer). And there is more I'm sure.
Bottom line is that it will cost quite a bit and probably isn't worth it since you can get a used rifle set up for these cartridges at a fairly reasonable price especially if you sell the 7 Rem. Mag. first. I just saw a nice used 7 RUM at a local shop for $385.00 with a muzzle break.
I hope that this doesn't offend you but I didn't want to see you waste time and money.
Best.