The quick answer is right around 1200 yards. The real answer is it depends on a lot of things. The first half of that 1200 isn't that hard; so when you say that 500 is easy for you I believe you. Truth is, 500 should be easy because frankly in the right circumstances it still is easy. The degree of difficulty sky-rockets right after that and a real 600 in the field is a pretty long poke.
Since you asked, my longest game shot with a .300 Win is a lasered 568 yards taken in Argentina on a red stag. Rifle was a Weatherby Ultra lightweight rebarrelled in a #2 Gaillard to .300 Win with a 3.5-10 VXL3 with B&C reticle. Load was 168 grain TSXs put up in Norma brass. Ordinary stuff, really. Just the sort of thing that makes a good general purpose hunting rifle. Since I was out of aiming points in the scope I was down to holding elevation with the infinity pin. Wind wasn't bad, estimated 5-6 MPH half force from the right.I run those numbers in my head using some tricks that I likely didn't invent but did stumble onto myself. Drilled it square through both shoulders and you could hear the crack all the way back to where we were on the valley wall.
The fun part was the reaction of the Spanish speaking guides, who it turns out were only joking about taking the shot. It took a moment to figure out that when one was pawing the dirt with his hand and saying "metros, metros" he was asking me to write down the distance in meters. Armed with the number word spread through the ranch until I was confronted by the owner who could accurately described as a giant of a man. I thought I was going to be killed for being so stupid but after he asked about the shot and stared me in the eye for what seemed like an hour, he removed his hat and bowed. Turns out that in the 200 years his family owned that ranch there was only one longer shot taken, and that was by a Argentinian sniper armed with heavy rifle and a lap-top. Last I heard they were talking about building a shrine, being the devote Catholics that they were. (OK, I made that last part up, but they were pretty excited about it). I got toasted at supper every night for the rest of the trip. They take their wine as seriously as their Catholism, so that may have been just an excuse to pound more of it.