I’m curious as to why you have such an extensive acoustic treatment program, but absolutely nothing on the front wall?
I at first though that maybe you were attempting LEDE, but that can’t be the case because you said you have diffusers on the back wall. What type of diffusers are they, by the way?
With regard to the asymmetrical room, alcove and window causing the image shift...I’ve worked with asymmetrical rooms that have windows or glass and openings to other areas/alcoves and have been able to get a strong center image without covering all the glass so long as the early reflection vectors are treated with absorption and all opposing hard surfaces have absorption on at least one of those surfaces to kill the bounce. Your window is (mostly) behind an absorption panel and has the glass covered by fabric...the alcove has an absorption panel in it to attenuate any possible resonance issues and is a good distance away from the listening spot (so any reflections coming from there are late arriving and relatively inert). I think you’ve addressed these potentially problematic areas appropriately.
Your listening spot is fifteen feet from the front wall (wall behind the speakers)
and that puts you almost in the center of the room...not ideal. Try moving the listening spot closer to rear wall by a few feet and also moving the speakers further into the room the same distance....maybe six feet into the room from the front wall for the speakers and seventeen feet for the listening spot (as a starting point). This will get you and the speakers further away from the alcove and reduce interaction with the window by moving the first reflection off of it. Don’t forget to relocate the absorption panels at side wall first reflection locations. This will remove a panel from in front of the window, and though it will no longer be an early reflection vector, I still think it a good idea to cover up the glass as much as possible...so maybe take the panel in the alcove and move it over in front of the glass.
Also, unless you have a few reference recordings you routinely use to test and dial in a system, you need some sort of reliable reference tool. I like this one...
https://www.audiocheck.net/
Michael