In order to set a div containing a transparent text image as the highest z-index in my document, I picked the number 10,000 and it solved my problem.
Previously I had guessed with the number 3 but it had no effect.
So, is there a more scientific way of figuring out what z-index is higher than that of all of your other elements?
I tried looking for this metric in Firebug but couldn't find it.