Just because you have a long action, doesn't mean you need to get a long action cartridge.
If the cartridge you end up deciding on, meets all your specifications but would have fit in a short action, I wouldn't be worried at all.
As you said 600 yards, many rounds will do this distance comfortably, could probably even get a 223 to be competitive at that range.
I'd be inclined to go with a 6.5 of some sort, not a barrel burning one and one that doesn't need much or any prep to get brass.
260Rem, 6.5x47L or 6.5 Creedmore are all good on barrels and give great performance at 600 yards and more. Creedmore is the only one that doesn't have Lapua brass but the Hornady brass is meant to be pretty good.
6.5x55 will also run with any of these rounds, but doesn't seem to have to the same cool factor so is often over looked.
A long action round worth considering is 284 Win, this round has a lot going for it. Will have better ballistics than the other three mentioned, also doesn't burn out barrels, but will recoil more and needs a bit of prep if you want really good brass as need to neck up 6.5-284 brass.
Decide if you want;
Cheap ammo
Little brass prep
Long barrel life
Blistering fast, great ballistics
Factory ammo available
Then see which round fits the categories you want, and don't think twice if its a short or long action round.
P.S, 284 Win is sometimes called a long action round, but you need to seat the bullet extremely deep if you use the high BC ones, often sacrificing a lot of velocity and making if more or less a waste of time.