It's not budget friendly, but since you're emphasizing precision in an environment where every bit of juice you can squeeze matters, I would suggest the Federal Terminal Ascent 175gr .308 loadings.
a few things to note, and an explanation of why I'm recommending such a premium round.
notes:
1) I've used it extensively in competition and hunting, and it is the only premium cartridge that feels actually worth the cost to me
2) You will need to use either metal mags (KAC, etc) or the Magpul red follower 25rd, designed for M118LR as the cartridge length is 2.83"
Reasoning:
1) accuracy. It has the highest BC available to a .308 factory loading without single-feeding and running hand loads, it has performed well in every gas and bolt platform I have tried it in, and is my competition load for that reason.
2) terminal performance. The design is very similar to the Trophy-bonded Bear Claw which was the basis for Federal's Law Enforcement ammunition line, because of its performance against barriers, particularly auto glass and other commercial glazing, which is traditionally a very difficult barrier. The solid copper base does an excellent job of providing barrier blindness and retained weight on target.
3) Reliability of terminal performance: The projectile will reliably expand even at transonic velocities out to the advertised maximum of ~1000y. This has been demonstrated multiple places, and provides for excellent terminal effect at most conceivable ranges and conditions that a LE sniper team might be called upon to operate in.
4) fully element sealed: Perhaps a nitpick, but the nickel brass case, sealed neck, sealed primer, and nickel coated projectile mean that short of being mangled somehow, the ammunition will remain usable and effective in harsh conditions.
It is expensive, but considering the potential benefits to your department, it may be worth the price of entry.
Lead sniper. No we are not that high speed. We currently have no sniper element at all. I have a military experience and a 1300 yard range that I can shoot on from my back porch. Aka a big field. 
