My 12BVSS had a similar condition with the front pillar and with the tang in contact on one side of the stock. I added about .030" to the front pillar getting it above the wood and added .005 clearance under the tang and it settled right in. I also bedded the recoil lug. I'm able to easily pass a cigarette paper freely all the way around, between the action and stock, with no contact under the tang.
It really made a difference.
My first thought was to bed it but I don't see the need any longer. SSS can take care of it if you go that route.