Maybe I need to remove some of the acoustic "cocoon" that I've created around the listening area.
I wouldn't do that, at least not as the first step. In the end, maybe you really are absorbing too much in too narrow a bandwidth, but absorption behind the speakers is usually a good thing that you can't have too much of. More likely suspects are the walls to either side of the speakers and the ceiling (especially if it's low). Ideally, you'll want to place absorbers in all three locations, midway between you and the speakers and a few inches away from the walls/ceiling.
(This is all to control flutter echoes and comb filtering, which will help stereo imaging. Unfortunately, these measures will do nothing for low-frequency resonances. For that, you'd need real bass trapping, which is difficult and takes up a lot of space. But it's more likely your problem is in the midrange and upper-mids.)
Based on your description, it sounds as though you're experiencing phase cancellations between that portion of the signal that's common to both left and right channels. If the center sounds fuller with headphones, that would confirm the hypothesis. First, make sure your speakers are equidistant from the nearest walls. If one is closer to a wall than the other, that'll skew the panorama and do weird things to the center.