I am by no means an expert on this, but I am researching rechambering a 308 myself.
I don't think you can go to a 7prc as the case is shorter, and you definitely cannot go to a 300prc as the barrel is only .284, not .308. Rechambering is simply redoing the chamber, not re-drilling the entire barrel.
You can have it re-barreled by a gunsmith or go to a remage barrel that has a barrel nut like a savage, so you can tighten the barrel up against you, go gauge, and then tighten the barrel nut. You will need to perform some stock work on the barrel nut for this, though.