It definitely seems to be a DC offset problem, with the left channel having a positive offset, and the right channel a negative one. This DC offset is being generated by your phono stage. The first thing you should do is reset the zoom level in Audition (right click in the dB scale to the right and choose FULL ZOOM), in order to make sure the recording scale is at the absolute center. Then try this:
1) The phono stage may need to be loaded with a lower impedance (10 Kohms to 50 Kohms), because the sound card presents too high an input impedance (100 Kohms or more). In this case try to connect a 22 Kohm resistor in parallel with every output channel at the phono stage. You will need a couple of Y connectors and a bit of creativity. Make sure you don't accidentally short the preamp's outputs to ground.
2) If the former procedure doesn't work, insert an electrolytic capacitor of 10 uF or so in series with each phono stage output terminal (keep all grounds together). This should block any DC in the phono stage, and allow you to record the signal. Observe its balance in the recording display. They should both now be centered at around -infinite.
It's much better to eliminate any DC offset before entering the sound card, in order to have a clean recording. If you wish, you can eliminate any remaining trace of it using the Constant Amplification effect at 0 dB, and enabling the DC offset compensation. Once you get a decent recording, it's time to begin looking for better coupling capacitors or a better phono stage.
Regards,