I have a Springfield Armory Geneso IL I got back in the early 90s. Built on a surplus WWII date forged receiver w/ new wood 7.62 barrel and spacer block. 100% reliable, beautiful, and my fave rifle. They are not common however.
Aluminum Spacer Blocks to prevent loading 30-06 in the magazine are made and available from Midway, Brownell's, etc. I have two steel Korean spacers. The Israelis and a South American country made them also. Otherwise, it's just a simple rebarrel.
They are out there for under $900.00. Sarco sells 308 kits. The top rifle in the photo is my "Italian T2" copy. Excellent shooter that I got for under $800.00 on GB a few years ago. There is a guy from near Green Bay, Wi who builds them for well under $1000.00 and sells them at the local gunshows.
As far a Navy 308, well anything marked navy carries a huge premium.