My experience is regular old document.elementFromPoint(...) works for absolutely positioned elements too, but it's sensitive to the "order" of the elements (which element is really "in front"). I've found that sometimes to get it to work the way I want, I have to explicitly specfy the CSS "z-index" (sometimes with a positive value of 10 or more) on the absolutely positioned element.
This is especially an issue if the elements have no background and contain just text, as all of them will be visible at the same time in the same place. From just the appearance, it can be hard to tell which one is really "in front", perhaps not the one you think.