I'm getting ready to do the same setup in our 'tek, and found a site that will probably help you with your problem. Most good name brand head units won't let you do DVD/Navigation controls while the car isn't in park, but the simple circuit here: http://www.mnsportcompacts.net/forum/showthread.php?94769-The-hands-free-way-to-bypass-your-parking-brake-wire should do the trick. Just uses a relay connected to the amp cut on circuit, which pulses the brake line on the radio, fooling it into working. If you've got navigation on your headunit, it may not bypass with this though, as some of them read your GPS speed, or use motion detection to disable those features.
Just bought this little unit off ebay: http://www.ebay.com/itm/120740223447?ssPageName=STRK:MEWNX:IT&_trksid=p3984.m1439.l2649
Gonna see how she goes. Currently trying to install the headrest monitors.
what model is the unit? I may have answers
This is quite the common question for me lol. It's somewhat of a chinese knock off. Here's a link to the deck:
http://www.lightinthebox.com/7--Motorized-Digital-Touch-Screen-2-Din-Car-DVD-Player-GPS-RDS-BT-Ipod-DVB-T-PIP-Steering-Control-SZC1904-_p90561.html
Don't know if it helps any with your answers, but other than what I know in my head about tinkering with it, there's not much to read on it.