I would snug up the action screws and all the scope base and mount screws. Go to the range, fire your couple of quick shots and then try the 5 dollar bill down the barrel channel looking for barrel contact on the stock.
While I do think you're asking a little much of the axis, I also think things can be improved a bit.
While I do think you're asking a little much of the axis, I also think things can be improved a bit.