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"Can you even see the target - not hunting - at 600+ without a scope?"

Absolutely. Remember that the targets, on the NRA Highpower course of fire, are HUGE. The target itself is almost 6 feet square. The black bullseye is about 6 MOA wide at all ranges, ie 12" at 200, (actually 13"), 36" at 600 etc. The 10 ring is about 2 MOA wide at all ranges. They are easy to see and easy to hit. The trick is hitting the 10/X ring consistently every shot.

The 6.5 has one big advantage over other calibers and that is ballistic coefficient. This is a measure of how easily the bullet moves through the air. .30 caliber bullets that are commonly fired at 1000 yards are 190+ grains in weight. You need a lot of case capacity to drive these heavy slugs fast enough to stay ahead of the wind at 1000 yards. The BC of a 190 Sierra Matchking is roughly .550. You need a muzzle velocity of at least 2500 FPS and most shooters want more than that. A Magnum will get you to 2900 FPS but barrel life will be 500 rounds or less and the cost of shooting a Magnum is prohibitive. Now look at the 6.5. A 140 gr Sierra MK has a BC of .540 and a speed of 2800 is easy to get, even with a case as small as the 6.5x55. Recoil wont pound your position around with the smaller caliber and cost is greatly reduced. Twist for a 6.5 should be 1-8/1-9. Rem factory barrels are Ok for hunting but they are hammer forged, which means they have to be tapered in order to get the mandrel out. I know no one that shoots a factory tube. Hammer forging also induces much more stress into the tube so they are unpredictable when heated.

I see quite a few fellows shoot "F" class with Rem 700 police rifles and they do Ok. The range is short (600 yrds) and with a little tuning these rifles shoot pretty well.