I live in VT and have hunted here for 40+ years. The woods and terrain is the same as NH. I started out with a 30-30, then went to a .270 then a 30-06. Have kill many northeast deer with these calibers.
I must admit, I think a .450 would be a mistake. Have you ever considered that you might want to hunt other places in the future? Elk, Mule Deer, Antelope, even western whitetails? You could be faced with 200-400 yard shots or longer and a .450 would be a challenge at those distances. The most important thing in hunting is shot placement and waiting for the clear kill shot. If you Force a shot with any caliber it can deflect.
With your budget, there are many options. 3k-6k will get you into many custom rifles. You can also get into a Weatherby Vanguard Series 2 topped with a Swarovski Z3 4-12x50 for $1,400. These are guarenteed sub minute of accuracy out of the box. With a 30-06 you can get a wide array of bullet weights to suit your needs. If you reload, even more choices. If you still want bigger, a 300 Win Mag or 300 short Mag would be an excellent choice. Both still offer many options with bullet weights.
Best of luck in your decision.
Last edited by Rob in VT; 01-15-2018 at 05:02 AM.