Can you include Open link: Same window (_top)?
Hmm that makes popup disappear in the preview but not when I preview in Firefox or Chrome.

I make pop-up layer menus for all my mobile sites and all I do is untick the 'close pop-up automatically'. The pop-up closes when the visitor navigates to whatever page they've tapped on. True, you do have the ugly little cross to close manually, but it's not in your face and no one has ever mentioned it when I've sent the site out for approval and testing.
I tried this but I don't like this default close button especially on a main nav menu. Also if you use same page anchor links it's still seems the same problem in that it won't close automatically, you still have to click either the default close button or a custom one. Not an iassue when changing pages but it is for the same page anchor links.