Your 7mm's will do the job easily, some individuals might suggest heavier bullets but those Hornadys will do the job, a deer is not hard to kill if you hit him correctly. What you might find makes a huge difference in long range shooting will be your scope. Many hunting scopes just don't do the job out past 5-600 yards as far as having adequate adjustment lattitude in their turrets. You don't mention your optics and mounts so not sure where you are at.
What we would do is setup large sheets of heavy steel plate (2'x4'), hanging them on old swingsets or sawhorses, paint the front white and shoot at them at longer ranges. Your rifle might beat up most thinner plate at 600, we use 3/8" and 1/2" at 700 yards and longer for our .308's with no damage. The bullets make a large splat that is clearly visible so we can get good zeros and see what the wind is doing to the bullet (can see hits all the way out to 1000 yards). We spray each splat white after several shots so that the plate is fresh and reshoot or move back farther away. We also have some smaller plates (6x6, 12x12 up to 16x16) that freestand on angle-iron bases. We paint them and knock them over at long ranges, makes for great practice also. Can also hang the smaller plates on the swingset or sawhorses to make them clang.
I find that practicing at 700 and longer makes 5-600 yard shots very doable for hunting, and that is about what you are talking.
Work up some drop charts and learn to shoot in wind and you will have confidence when you take a long shot. You will also need some good rests, an adequate laser rangefinder, and a partner to practice and hunt with to really enjoy this game.
