OP do you really need the threaded barrel? If not, then the Tikka Varmint model has the same contour as the Tac and CTR, and if you're going to a chassis anyway the stock won't matter.
I am finally getting around to building up my 11 year old Tikka Varmint with a KRG Bravo, Warne 20 MOA rail, and Vortex Razor HD 5-20x50 mil in a set of 1" Seekins rings. All told it will come in at the low end of your budget depending on what Tikkas go for nowadays-mine was $750 in 2007.
Varmint has a heavier contour than the Ctr.