As Peg noted, the 7-'06 to 308 would be a piece of cake. Same casehead size, so just a barrel change. The 7mm-08 is supposed to be a VERY accurate round, (never shot one), and has better sectional density than 30 cal. It's also a factory load so ammo is available over the counter.
With the 300 BLK, you are dropping down to 223/5.56 head size/length. That is going to be a larger operation than just a change in the extractor. Even the '06 bolt head is going to be way big.
What was the original 8mm? 7.92x57 Mauser or 8mm Rem Mag?