6.5PRC seems just fine as a hunting cartridge, especially when one considers that the 6.5CM was designed for the AR10 platform for shooting out to 600 yards in matches.
PRS varies hugely in range, out towards 1,200 yards. And your first shot counts, no sighters.
Gunwerks developed the 7mm LRM, 375 Ruger necked to 7mm. Available in their hunting rifles, just not for $1,100.
Why not re-barrel an existing rifle? Should keep you under your budget, if you have time.
Get to reloading. 375 Ruger brass can be had. Dies should be available from Hornady, and possibly Redding.