Add pointer-events: none;
to the overlay.
Original answer: My suggestion would be that you could capture the click event with the overlay, hide the overlay, then refire the click event, then display the overlay again. I'm not sure if you'd get a flicker effect though.
[Update] Exactly this problem and exactly my solution just appeared in this post: "Forwarding Mouse Events Through Layers". I know its probably a little late for the OP, but for the sake of somebody having this problem in the future, I though I would include it.