The back of your subwoofer should have a low level connection (or a pair, R and L). Most newer subs have an "LFE" connection, which I'm assuming is what Denon means by "direct mode". Either the R or L low level connection should possibly function as an LFE input (please, someone correct me if I'm wrong in this case, as I've never set up one of these subs). Anyway, if you simply plug a subwoofer cable (RCA-type) from the subwoofer pre-out of your Denon into either the R or L low level input, then the simplest way to set it up is with the first set of settings in your post. If the R or L can't function as an LFE input (which I'd be surprised about), then you'd need to hook the sub using the speaker-level connections (the spring-loaded ones on the back of your sub), and Audyssey would be unable to correct for the sub; you'd have to do it manually by setting the crossover, phase, etc. using the knobs and switches on the back of your sub.
Two things are infinite: the universe and human stupidity. And I'm not sure about the universe. -- Albert Einstein