Mitchell,
I've got to agree with Mikey. There's no way you can build a custom Mauser .308 for $600, starting with a mil-surp 8mm. Just the cost of rebarreling with a decent tube would make the project unfeasable at the given price.
I would stick with the 8mm as he said, but I would opt for an inexpensive drop-in stock like a RamLine to save weight. (Of course, with some rasps, files and sandpaper you can come up with a pretty decent sporting stock from the military one. They call it "sweat equity.") And, with practice, you can get used to the military triggers. I have done so. Saves a chunk of money as well.
My own 8mm sporters, so configured, are more powerful than any .308 with the proper handloads, and, if more power is wanted, one can simply ream out the chamber to 8mm-06. Or, even better, go for the Improved version.
In any event, good luck with your project. Happy shooting.