edit. didn't read all the updates before posting this so hex168 and Duke already touched the subject of time-intensity trading. I'll leave the post here though as there is some more points.
That would imply that the soundstage is not very stable for one reason or another. My experience is if there is not any interference, there is quite a bit of freedom to move about the desk (or console in this instance) without having he imaging change appreciably. Obviously if one moves far off to the side the sound collapses into each respective speaker, but ideally the sweet spot should be large enough to be useful. I don’t know of all the factors involved, but I would surmise the listening window of the speaker plays an important role. A wider radiation pattern will mean that the SPL level heard by each ear does not change much with movement within the listening window since the pattern is flat and wide (edit: but worth noting there will be more side reflections). The ITD will still be altered, of course, but this removes ILDs associated with small head movements. But with a narrow radiation pattern and the need to directly face the speakers, there are potentially large SPL gradients once one moves away from the mid-position, and this induces ILDs as well as ITDs, which is likely to induce additional image shift. Just some food for thought, perhaps.
With constant directivity narrower coverage speakers one can use toe-in to beat this, somewhat. Its got name "time intensity trading" I think. When moving to side from center line between speakers we get closer in time for that side speaker but also further off-axis and get less intensity, sound level decreases. And the opposite happens for the far side, we are now more on-axis so more level to compensate the fact we are further in time. This should should keep image stable. On the other hand less toe-in is completely opposite, as moving to side one gets closer to the speaker in time and in more on-axis so also level increases while further speaker gets further in time and level. These should guarantee phantom center fast collapses to the closest speaker, unstable image.
I have such speakers, but I reckon pattern is too wide as it doesn't work as well as I hoped, although image is quite fine for big area the sweet spot is still small where everything stays in place. Here is what I mean by that, I can move quite a bit before phantom center collapses to the closest speaker, this is good. But, to my disappointment, phantom center moves in front of me, with me, which is interesting, but of course far sides of the image is still bound to speakers which kind of skews the whole image. I think trade between time and intensity is not enough to keep the center image in place, intensity should change more than what I now have, which means narrower directivity.
There is also benefits recarding 3D imaging but require more symmetric setup than I have. ~45deg toed-in speakers radiate very little to the closest boundaries and quite strongly to opposite side of room. Trick is not to have acoustic treatment to keep these late reflevtions to have envelopment/spaciousness that kind of suffers with narrow coverage and toe-in. For people chasing 3D imaging this shouldn't be a problem though, I think. In my situation, big room asymmetric setup these dont help so much so envelopment isn't too good, image is though. I could toe-in less, but it goes blurry big image.
As disclaimer I haven't listened wide coverage speakers long time and never in this room.
ps. just add third speaker as real center and the problems should go away. Too little envelopment? just add rear speakers to create some.