I feel your pain, 4040. I have a Remington Varmint Synthetic short action in 308 with the standard short action magazine which will accept and feed OALs no more than 2.840". In order to get VLDs closer to the lands, I have to set my OAL at 2.9 inches, which still leaves about .050 inch to the lands. That precludes feeding from the magazine.
Some VLD bullets and secant ogives just don't like that much of a jump. Big green puts a lot of freebore into their short action rifles as they come from the factory.
Yep, it is possible to put a 308 barrel on a long action receiver, but it might be better yet to have a new barrel installed on what you have already. The reason I say this is that you might have issues feeding factory length rounds from a long action magazine.
If you notice, some of the Savage models use a long action for 308 length cartridges, but they put a block in the back of the magazine to correctly orient the cartridge.
In reality, the reason the army went to a long action on their sniper rifles initially was because they wanted to use proven match 30/06 ammo, then found out they didn't have enough of it on hand. The 300 Win mag was also considered, but that would call for a change of bolt head, magazine and barrel.