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Did you try to adjust the SA firing pin? I adjusted mine on my Stevens SA 7mm SAUM head bolt.
If you are going to put a 270 WSM on what is now a 308 Savage short action you don't need another firing pin. Savage has long action firing pins and short action firing pins....the WSM's come on short actions. If you are getting a slight protrusion now it is easy to adjust for a bit more. I converted a standard Savage short action to a 300WSM but I didn't want the Control Round Feed bolt head....so I took a 7MM Magnum bolt head and cut the shaft to the same length as the regular short action bolt head.
That's why I went with the shortened 7mm mag bolt head. Just less hassle and expense all round.