Unfortunately you don't have a good option. I have a 0404, 0202, and Tracker-Pre and they all have problems with the headphone jacks.
The front panel headphone jack is pretty cheap, and it's an "enclosed" type so you can't get inside to increase the spring tension on the connections. It's the preferred output jack since it has much lower output impedance than the back panel jacks. (About 20 ohms vice 600 ohms.)
The back panel 1/4" jacks are balanced three conductor types so you'll only get one channel. Is that what you meant?
I would continue to use the 3.5mm output jack. It's output resistance is 560 ohms, but should work okay for most applications.
Cheers,
Dave.