Just wanted to chime in more now that work cleared for a minute...
I suspect that the cover/baffle under the sub is to designed to "shrink" the trunk size as far as the sub is concerned. It would slow the airflow and create some resistance. I've had two thoughts for that baffle...
1. try to make it work better by either sealing with dynamat or stuffing with poly fill.
2. replace entirely and build a lightweight box. Hang and seal it to the deck under the factory location.
Overall, I'm extremely disappointed in the THX sound system. It is not up to par with other THX systems in other Lincolns or even systems in less expensive cars. I hope that improving the sub will make the whole system sound better, but I'm not sure. I've read that disconnecting the center dash speakers improves sound quality, but I use my Sync, nav, blutooth, etc daily, so I'm not sure that's a good option for me.
Curious about the audio controller with line out input. Can't you just buy an amp that accepts line out inputs instead? I don't think it would add anything unless you also purchase the remote control. This will be the first time I've tried to modify a factory system so my knowledge is very lacking. I'm used to just ripping EVERY factory component out and replacing.