You should have done less drinking and more research.
Could you buy two rifles (both similar model Savage) as donor rifles? Yes.
Could you swap barrels? Yes.
Would that give you a 6mm-06? No.
Would that give you a .308 Win? No.
The .30-06 case is almost 2.5" long while the .243 case is barely over 2" long. See a problem? No? Then...
What it would give you is a long action .243Win that probably would have the extractor groove and sights out of alignment and a short action .30-06 that you could never load a magazine for, nor chamber a round. Again extractor grooves and sights might be misaligned.
At the least, if you weren't drinking heavily during the builds, you would need to ensure extractor groove and sights properly indexed and then ream out the 6mm barrel to allow the .30-06 case to chamber (IF there was enough meat in the barrel root for this).
On the .308Win rifle, you would need to cut some of the barrel off, cut a new shoulder, and re-thread it, cut a new extractor groove in the right place and ensure you took the right amount off for sight indexing. Once you did all of that, you would need to ream out the chamber for .308 Win headspace.
Luckily, you stopped drinking, started thinking, and posted here. I hope you do some more thinking. I mean, if you bought Tikkas, that'd be a whole different story...