I'm not sure how helpful this is going to be, but my concerns that it wasn't going to be helpful kept me from responding last night, but I woke up with this post still on my heart and so I'm going to give it a whirl anyway.

First, the only thing I can tell you about integration is that it is my one and only deal-breaker in therapy. The very idea feels like murder/suicide.
Fortunately, my therapist is against the idea for us. Here comes the part that I can't figure out how not to say but is the reason for my reluctance to respond...it sounds so...pfft, like bragging or something, and I certainly don't mean it to come out like that, but it feels like a necessary precursor to sharing my thoughts about your experience.

My T says that normally she would be pro-integration but not with us because she feels that we have become more than the sum of our parts. While it hasn't always been this way, we work together extraordinarily well and have for some time. Really though, I have some challenges in loving myself, but (even though it's a physical impossibility) I'd take a bullet for any of my alters, and they know it. Though she's never said it, my T sees our relationship as the impetus for any and all self-care. So anyway, that said...

What you're describing sounds less like integration to me and more like strengthening co-consciousness. Maybe co-consciousness falls on a continuum and the far end IS integration, I really don't know, but getting three of them in a room and getting to know each other better...well, it's the first step to a better, stronger relationship. I mean, it's why we date (or dated) right? Get together with someone one on one and spend some time with this person, getting to know them so we can figure out whether we want to be in a relationship with them. With our alters, we already are in relationship with them - "you can pick your friends but you can't pick your relatives" kind of thing, but communication is necessary to improve any relationship.

Note: Someone please remind me not to post in the morning before coffee...

ahem, okay, back to it...anyway, so how is this going to change anything? Well, I don't know. But it does sound a bit like family therapy. Often members of the family have individual counseling sessions and then they come together and have a family session where they try to see things from each others point of view, work out grievances, learn to respect and appreciate each members place in, and contributions to the family, and look for solutions together. Yeah...strikes me as family therapy rather than integration.