After reading all of this, the desire for a decent M1 Garand has reawakened. The rifle my father carried during the Cold War; must have, someday...
(He just missed the Korean War.)
While it is not an autoloader, the Browning BLR can be had in .308, and has detachable box magazines. For those who dream of extended, higher-capacity BLR magazines, well, the lever would hit an extended magazine. A 'smith or skilled machinist could probably extend a BLR magazine, by a small amount, that would just leave clearance for the lever. The newest generation of BLR, extant since at least the mid-Nineties, have magazines that drop free.