Why not show the overlay when the user performs an action rather than after a delay? For example, displaying it when the user scrolls to the bottom of the page content. Or half way through but display it in a way that doesn't interrupt reading (as a fly-out from the right hand side perhaps)?

The optimal time to display something like that is when the user is engaged, interested and open to receiving more content from the site - not "after an arbitrary period of time".