Move your sub

The key is to realize that a phase knob can only add delay.

The real magic to sub integration is being able to delay the main speakers so that you can have the sub where it truly performs the best in the room without compromise.

Also, crossing over a pair of subs to your mains, regardless of how “full range,” will almost always be best.

Oh, and the realization that bass trapping (when done right) is crucial.  Completely different than room correction.

Oh Lordy, my bad. It is indeed Steve Guttenberg and not Mr. Dudley. A simple error rather than oncoming senility.

Yeah…Steve…this video does lack Art.

I had a real challenge integrating a pair of JL Audio F113V2 subs into my system, as the room had this "single note" it added to the music (regardless of what the bass player was playing), not a problem before I added the subs.
I found that moving the subs to a position in the center of the room, behind my sofa (and listening position) solved most of the "room issues", but the visceral listening experience was "off"...the tonality of the bass was not "directional", but the "feel" of the bass came from behind, while the music came from in front of my listening position.
Ten bass traps later, I positioned the pair of subs right next to the main speakers and once properly "tuned", all is "good".  The sound and feeling generated by my system is "consistent".

@contuzzi

true, the phase adjustment does add delay but it has always worked for me.  my typical method is to reverse polarity on the sub and take an RTA measurement using uncorrelated pink noise.  It is easy to spot the main speaker's roll-off frequency.  Adjust the crossover on the sub to match, measure again.  There will probably be peaks or valleys near the crossover frequency.  Adjust the phase angle to flatten the response and then adjust the level by ear. 
Another important consideration is to avoid pre-amp connection to the sub and always use speaker level connections.  Much better for the sub to see the amplified signal that is identical to the signal the main speakers see. 
I use this method and have a completely smooth response curve with one sub from 20Hz through the midbass region.  It is non directional and bass comes directly from center stage- no peaks in the sound and as you said absolutely no room correction or EQ.  It sounds perfect.