Absolutely no way I would leave the stock contacting the barrel. I have owned 3 Tikkas. Had to dremel/sand the stock on all of them, and all of them shot sub-MOA once I was done, both with factory ammo and handloads. All 3 shot better after fixing the stock than before.
Fix the stock contact issue, buy a pic rail or DNZ one-piece to mount the scope, and it should shoot fine. If it doesn't, try a different scope. If it still doesn't, try 140 ELD-M ammo. If it still doesn't, send it to Tikka (I would be floored if you make it this far).
My guess is the rings/base causing the issue. I used to not listen to folks who said to buy quality rings/base, and I didn't realize that I eventually paid the price for it. I don't necessarily go buy expensive stuff now, but I do stick to well-made, medium priced components or I'll just go drop the coin on the good stuff.