I went to a sign makers show a few months back and was introduced to a LED light that was in a tape form. Approx. 1/16" thick, can be ordered in any width, length, or color. What I liked about it was this exact application, because it can be stuck to the under side of the top directly instead of mounting to the cabinet box and worrying about shadowing. I will try to find the info on it, but it was very cool.
John