Just a thought experiment here...
I've always liked the AR-10. Being cheap I'll probably never buy one, but I could build one... sort of. It wouldn't have to be a real AR-10, just an AR-pattern rifle in .308. For that matter, why not .30-06?
Milling an AR receiver from billet has been done often enough. I've found several sets of drawings on the 'net.
As a first approximation, just stretch an ordinary AR at the magwell, widen enough to take an FN-D .30-06 mag, do any other fiddles needed. Use an ordinary AR trigger group, stock, pistol grip, etc.
That leaves the question of an upper. The AR uses a 1919-style barrel extension and a multipiece bolt, which wouldn't be all that difficult to upscale to suit the larger cartridge. The barrel extension and bolt head could be broached in the lathe, using the carriage or a tailstock fixture. Practically everything in the upper would have to be handmade.
Probably not worth the effort, but an '06 would be way cool.