You almost couldn't find a 7mm RM that won't do what you want done at 450-500 yards. Go with the rifle that fits and feels best to you. I've had my old tang safety Ruger for 35 years and that 7 kills stuff pretty well. It is glass bedded and had the trigger done and shoots the 150 grain TTSX or NBT loads under 1/2 inch for 5 shots if I don't screw up too badly. There are several rifles way under your price limit that guaranty an inch or less Tikka, Weatherby Vanguard, and others but I like Brownings and wouldn't hesitate to get one if that is a rifle you like. As long as you load your own rounds and use a decent scope you should be able to get your 7 dialed in to hit deer vitals at 500 yards from a good rest all day long. Past 350 or so the wind is the most important factor.
You will find that most of the long range shooters will dial in their scopes for ultimate accuracy. At under 600 yards even those ranging reticles like the Zeiss z600 or 800 will be accurate enough for deer and elk hunting. The 7 is a good flat shooting gun that tends to be pretty darn accurate and doesn't kick much in comparison to its performance. There are several calibers that will do what you want, lately I think if I were buying a do everything rifle I might go with a 300 WSM and stick wth a short action that is very efficient shooting a 180 grain bullet near the velocity of the 150 grain bullets in the seven with similar felt recoil.
