The 600 would probably work, didn't it origionally come in 308 as an option. There were also 600 and 660s with a 6mm rem. I would suppose that it could do a 260ai with a decent col to boot. That would be one mean little compact long range rig. I think hs is making a stock for them, that is the hardest problem with the 600 and 660 actions is the lack of stocks available.
I put together a 600 for smaller folk a couple of decades ago, closer to 3 actually. I used a Brown Precision in Kevlar. They still list this available on their site. It's qualified with a comment about using a 700 trigger guard. I don't remember any particular difficulty getting it to work.
Mine is in a 6mm Remington, and I don't see a reason the 260 won't work, unless you require a longer action for seating bullets out longer.