Hi...so here's what I think, take or leave is totally fine. I said a lot of it in my other reply there, but several things come to mind regarding your post.
One is that I don't have people coming up to me and saying they know me by different names either... tho sometimes people "knew" me, when i had no clue who they were. Forgetful? Dunno.
Another thing is that "integration" is an old term. And old therapy goal, and mostly outdated now. It is (for most) a far better goal to get "everyone" or all your sense of Self on the same page and to communicate and have the same goals - like you said; one knows something is wrong and wants what is best for your boy, one doesn't think anything is wrong (i also have that)... one feels young... etc. It is more important for each to have a voice, to express their thoughts and emotions and look at root causes and to come to agreement as a whole because all parts are needed to the whole. Like 'the sum is more than the total of the parts'.
Also, while EMDR is a useful trauma tool, it is often very hard to use with dissociative people - instead of working to resolve issues, it seems to help us dissociate more. So your T is right in that regard that it isn't the right time. In fact, I have found that EMDR is actually more useful for bringing me out of a state. Something you might talk with T about.
Hope some of that is useful. best!