I have to agree with Jerry.
I wouldn't want a chasis rifle as my hunting rifle, and you'd definitely want to re-prioritize where your money is going. 400Yd is not a huge distance, harvested a few deer out to that distance with 9x scopes. In your position I would be looking at a high bang for the buck rifle with good glass on top.
I love my Weatherby Vanguard S2, probably the best rifle you could buy for under $1000. I've seen them listed new for $680 from a site sponsor, that would give you $1300 for a scope and rings. I can make my S2 group 1-1.5" at 200 yards with my hunting reloads (IE. Not really trying hard) so the accuracy is there.
When I was shopping for my 10BA Stealth I looked at a lot of glass and ended up going with a Sightron SIII($1400), but a close second was the Nikon X1000 then a Viper HST, both of these are in that $900-1000 range. With either the X1000 or the HST you'd be looking at $1700 plus rail/rings. My want for the rifle is a bit different from your's though, I want to hit steel at 1000m.
TL;DR - Go big on quality glass, 400Yd's isn't that far and you can't hit what you can't see. Most rifles can shoot accurately to 400yds, and there are cheaper options that will let you invest in a good scope.