I'm down this road actually, my budget is about the same, for PRS competition on the open division.
Honestly THE option is to go with a Tikka 223 IMHO.
Savage wil offers something acceptable, but the action is far from being as smooth as a tikka... And you'll end up putting considerably lot of money on a Savage.
Missed a Tikka T3x Varmint Stainless a week ago... Danm.
My plan is to found a used tikka, ideally with a tikka heavy barrel... In the future switch the barrel for a IBI prefit. Change the stock for a MDT XRS ( my other Tikka PRS rifle in 6.5CMhas this chassis also and I like it).
Good luck buddy!
Evil Dark