Having never messed with wordpress before I wouldn't know: just to clarify your saying you can't alter the html? If this is the case you may want to look into using the css properties of z-index and display.
z-index sorts the document into layers like z-index:-1; or z-index:200; or whatever number you like depending on how many layers there are. Try a high z-index number first.
Display is the box displayed by an element which shouldn't matter here but sometimes this is a remedy for IE issues. display:inline; should be fine.
Try altering the css for the parent divs that contain the actual content and something good should happen