Well... if it's TV out then why can't you just run the LCD that out instead of the onboard? I wonder if the output only goes active if there is video playing, or if it's essentially cloning. It might be easier to wire something to the Dock Connector rather than the on-board too. Though, you'd need an LCD that could modulate Composite video...

Though a nice ribbon cable to do the job would be quite sweet.

Anyway, heres the pinout for the dock connector:
http://pinouts.ru/Devices/ipod_pinout.shtml

Hope it helps a little.