+1 for what @stug has stated.
Cold/clean vs hot barrel can end up with 1st shot being out compared to subsequent shots.
But your description sounds more than the difference in a fouling shot.
Tapping scope - I'd be carefully checking for loose rings/bases. What torque are you using for rings screws ? Bases ? Get a torque driver and check them.
Action screws - check these are not loose. You need a torque driver. Also be careful not to overtighten the action screws in the standard Tikka stocks as you can crush the stock & you end up with problems with the free floating recoil lug. Tikka's rely on that free floating lug working correctly. I use 35lbs as max torque on action screws with Tikka plastic stocks.
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