Same here. I am also cross eyed dominant. Left eye:20/25; Right eye: 20/30. With my scout scope setup I have to blink the left eye other wise I see the barrel and front sight.
More importantly is the comb height. Try this: Focus on a target, then shut your eyes and mount the rifle. When you open your eyes you should be starring through the center of the scope. If you are not, get out the foam rubber and duct tape and adjust the comb height until the test works. Interestingly, even with low scope rings, I have to raise my comb height to make the test work(with the scope mounted in the conventional position). In the scout scope mounting position, an adjustment might not be required.
In my case, with pistol sights, I also must blink because I am not that heavily dominant.