Shakedown, the "subwoofer" main outputs on the back of your Coda are exact duplicates of the "preamp" main outputs. Just different labels. In theory, the Woodmeres should give you all the low frequency bass you need. In pactice though, as things are now, it won't be well controlled low bass (good damping), unless you get the amp(s) next to the speaker(s). If you keep the Coda near your listening chair, you'll be running rather long speaker cables, which ruin good bass transient response. If you put the Coda between the speakers, that's a little bit better solution for good bass control, but incovenient from a user standpoint.
All this is a good argument for separate components over integrateds, which IMO are best reserved for bedroom systems. In your situation, you'd get a lot better performance out of your main speakers by using a pair of monoblock amps next to the speakers, and preamp and sources next to your listening position. A preamp preferably with balanced outputs to drive longer cables to the monoblock amps (although with well designed/shielded single-ended cables, you can go up to 40 ft with no problem.) As things are now, adding a subwoofer won't do anything to improve the (somewhat less than optimum) performance of your Tylers. So I'd work toward improving the relationship between your main speakers and the amp(s) that drive them.
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