You might want to consider some of the lower light type plants and flowers, like are found in the forest understory. The Conservation Department in your state may have plant lists of shade tolerant plants. They usually aren't as popular as the full-partial sun varieties but they are out there.
I actually do have a few things like that on the other side of the yard. I think a couple of things have happened though with the "sunny" side. 1) the trees have grown more so are providing more shade and 2) I think there are two in question that are leaning more since the hurricane and thus are covering more area. They're coming out this summer as soon as I win the lottery.
wonder were I could find someone that works for "that" department...;-)