I think our suggestions may be more useful if you clarify that you want to compete or just "be able to engage" targets at 1000.
If you seriously want to compete at 1000 with a 308, I suggest a 24-30" tube. I highly suggest against a suppressor as well because if you are competing at 1000 on a regular basis, you are more then likely going to be shooting an F-class match or a similar style match. There is a reason you don't see too F-class guys running short barrel guns with suppressors. In those type matches you want to take out anything that may effect a string of fire and a suppressor/mirage will do that.
If you just want to be able to engage or train to 1000 yards, then a 18-20" will definitely get you there. I speak from experience because I've taken my old shorty Surgeon (17.5") to 1100 yards with a 178 bthp Hornady. Did I make hits.... Yes. Did miss WAY more then I hit the target....yes.
Speaking from experience, I started in this game with a short barrel because it was "the cool" thing to have at the time. None if my bolt guns are under 22" now, regardless of caliber. I will have another shorty soon but its definitely a niche specific gun, and that's the only reason.
If you do decide to remain with a short barrel, I highly suggest moving to a 6.5 Creed or X47 Lapua and run the Hybrid 140's. You will give up some speed but ballistics will still be far superior to a shorty 308.
If you decide to stick with a short 308 then my second suggestion would be to run the 185's with MR Pro 2000. You would be taking advantage of every you can to enhance the 308 cartridge with that set up, just don't go out expecting to set the range on fire with head shots at 700 yards in multiple cross winds.