One way around that is to make a stop
at a field within that TRACON's airspace.

I know someone who pulled this trick on NYC TRACON once, but he even
had the nerve to call them as he neared the airport he'd file to, and
ask to change his destination to where he really want to go!
Apparently, there was much sighing from the controller, but in the end,
the pilot got what he wanted.