Just some descent range run and gun stuff.
When Trijicon announced their Accupower 1-8, the Scar Heavy was the first rifle that came to mind. It can be had for a little over $1200.
For under 1k I would look at the PST 1-6. If you can stretch the budget, I would look at the accupower 1-8.
My Scar 17 is my favorite rifle, but I struggle with the optics selection for it. The gun was designed as a battle rifle for exactly what your talking about "run and gun out to 500". Problem with mine is it shoots to straight, and I end up doing other things with it. I originally out the Razor 1-6 on mine, as my "If I had 1 rifle to last for the rest of my life" type rifle. That scope didnt last long before I realized this thing shot almost as well as my match rifles, so not wanting to dump the original plan for the rifle I swapped the 1-6 for a 2.5-10. Then I started using it at even longer ranges, so I ended up with a 4-16 on it as now its a hunting rifle. For me with the rifles capabilities, the 2.5-10 was the sweet spot. Rifles capabilities have nothing to do with how you will use it, and your use trumps capabilities, which is why I would go 1-6. The reason my rifle went through so many changes is because as I learned capabilities I modified how I used it.
Hopefully that made sense.
I bet if you get out and shoot it a bit more you'll be just fine going beyond 600, but who knows I don't own a scar. I do know that a 16" bolt gun can do just fine beyond that though.I had very similar experience to yours. Started with Razor gen2 1-6. Very good scope and does well for Scar17.
Then went to Nightforce NSX 2.5-10. 2.5-10 i found does well for me out to 600yds. Much beyond that range, short barrel 308 is lacking.
I would think an ACOG would be a good fit for your budget and the distances you plan to shoot.
I bet if you get out and shoot it a bit more you'll be just fine going beyond 600, but who knows I don't own a scar. I do know that a 16" bolt gun can do just fine beyond that though.