My dot is very small and I think that's what make it work so well. Leupold Target Dot with Fine Cross Hair reticle.
Also, one last piece of info about my Sporter system. I use a screw-in cap on my eye piece with a small hole drilled in the center. Then I also have a cap on the front with a hole about twice the size. This accomplishes several things. It makes me place my eye in the exact same position for each shot. Also, I believe it has an optical effect sharpening my image. It also cuts down on the light coming through the scope and helps reduce eye fatigue. After 3 or (even more importantly) 6 targets this really helps.
Good luck!
I have too, a small target dot on fine crosshairs, good!
Funny enough I have on most of my scopes a cap with reduced diameter, as you described, to cut down light and increase depth of field.
But never found caps that suit the Leupolds. Did you machine or bought them?