If you like the 260 Remington,
Savage makes a factory target rifle in 6.5-284 which has been a hot cartridge in 1000 yard shooting, but has seen a bit of shift from to the 6.5x47 Lapua (similar to the 260 Remington) and to the 284 Winchester. The nice thing about the barrels is they can be swapped very easily due to their barrel mounting system.
Remington most definitely makes a bolt action in 260 Remington, but unless you get one of the 40x models from the custom shop, .5 moa accuracy out of the box would be hit or miss.
While the original post is old, I see updates are rather current. If you are thinking you want custom, but are nervous about what can be habitually long wait times when you custom order a gun, the best solution is to get all the parts together (action, stock, trigger, barrel, etc) and then bring into a skilled builder for final machining and assembly which can be turned around quickly (within a month). Most custom builders get backed up waiting on components like stocks which can take 4 months once ordered. One barrel maker quoted me 6 months for a barrel.
As a 1000 yard shooter, I have learned to just go to brunos shooters supply who stocks an assortment of high end actions, barrels and mcmillan stocks so you can pretty much get everything quickly.