I don't know if this will help, but I have been experimenting, getting ready to paint an F-14 kit, and the underside will be white. I have been experimenting on a kit I pulled from under the bench.
With this one I rattle-can primed it, then preshaded a flat black. I did not preshade it very dark, I could have put on a heavier coat. The random black was in hopes of coming out with a mottled/faded look.
And this is what it looked like after laying down white.
I don't have a camera that will take decent pictures, so these may not help at all. In this case, I never really got it looking white, it still looked more light gray.
My next attempt will be trying what DoogsATX suggests, beginning with a black base, and trying to slowly build up the white. I am experimenting at the same time with thinners, which does not make it any easier on me. Probably my biggest issue is going slowly enough with the final coats. If I am not too embarrassed, I will post more pictures.