Savage actually makes two different size firing pins, small and magnum. If your action used to be a 308, you probably already have the small firing pin hole.
I have a 6.5x47L built on a custom action, no primer issues at all. I also have a 6x47L on a 700, and I had cratering from the beginning, but only one pierce primer in about 300 rounds so far. I went with a heavier firing pin spring and the cratering disappeared. Cheaper than bushing the pin hole, but does make the bolt lift heavier. I will probably end up bushing anyway.
In your case, both methods will work if you need them. Bushing the hole is even easier for you since the bolt head is removeable.
TL;DR Use CCI primers and see what happens.