If you can wait a bit, the new S2H scope from ZeroTech looks to be the exact scope you're looking for. It's not available to buy today, but you can get it pre-ordered on the Shoot2Hunt website. I have one on order
If you need something today, a SWFA 3-9 is a very good option. FFP, as robust as anything, and surprisingly good optical quality for the $600 price. I love mine and it is way better than the price would indicate. No issues shooting to 800+ with it.
I like my LRHS, but the donut reticle is one that quite a few people don't like. Mine is the 3-12 which are really hard to find.you can find the 3-12 or the more common 4.5-18 used for under a grand fairly regularly.
The Maven RS1.2 is at the very top of your price range but worth looking at if you need something right now and really feel the desire for more magnification.
A 7PRC recoils a lot (relative to what most of us hunt with at those ranges) and to stay in the scope, even with a brake (eww) or suppressor (yay), you'll likely need to be in the 6-9x magnification range at 700 if you want to spot your own impacts. A scope that goes to 15x or 18x won't be much help in field shooting on that rifle.