You would be amaze at how much of the objective can be obscured without affecting the sight picture. Try it out. Look through your scope and block the objective with 2 fingers. I can block the top 1/3 and the bottom 1/3 and still have a perfect sight picture with a Leupold 3-9 x 40. Leupold sells a 50mm objective with the bottom 15-25% trimmed off for low mount applications.
I mount my scope really low, and use a cover on my can. The only time I can see a haze at the bottom of the picture is at 3X, anything more than that and it disappears.