You cant use light and soft bullets at close ranges woth the 7mm Rem Mag at full speeds, they'll blow up on impact with low penetration and cause slow kills. These bulleta are the 139gr SST, thw 140gr Ballistic Tip, 140gr Sierra Game King SPBT, etc. They are going to fast and dont penetrate as required to produce a fast kill.
If you might encounter close up shots its beat to use a heavier bullet like the 160gr Accubond or 162gr SST, I would go with the 162gr SST and you can go for behind the shoulder shots if you want to avoid meat damage. You'll turn the lunga to jello and get and exit wound, and drop the deer on its tracks.
If you still want to run a light bullet and fast then use a 140gr accubond, but, if meat damage is a concern, then use a monolithic like a hammer bullet, a 131gr Hammer Hunter or 136gr Sledge Hammer and you're set.