Remington had a 6.8SPC Model 700 rifle that they called the Tactical. Basically the same gun as the LVSF (light varmint stainless fluted), but blued metal and a gray stock with black web. They also had a 700 with a heavy 26" stainless bull barrel called the 700 Special something or other, essentially the same as the Varmint models with composite stocks. You can still get the 700 LTR in 6.8 as well. Prices on the first rifle were around $700, the heavy barrel prices were $800 or more, and the LTR is $850-$900. I had read where the Model Seven was going to be offered in 6.8, but don't know if they have yet. You can get a Custom Shop Model Seven in 6.8, you're looking at probably $1300 on the low end to as much as you want to pay on the high end.
If I wanted a 6.8 in a bolt, I'd get a CZ 527 in 7.62x39 and have it re-barreled. A little extractor work, and you'd be good to go. The 6.8 feeds well from the 7.62 magazine, and even if you went with a stout barrel, you'd still have a petite rifle suited to the mildness of the round. One of the test rifles that Hornady used in development was a CZ with a Schneider barrel, and the couple of articles I've read spoke well of the rifle and the round together. Shop around a bit and find a good used rifle, any good .270 cal barrel and a decent smith to put it together, you would have a sweet rifle, either cheaper or in the same price as the 700, but a better quality piece.