I can really hear how very very hard this is for you to manage - not at all the lovely “found my forever family” stories romanticised stories they sell at information evenings, but much more realistic in terms of your little boys response to being repeatedly picked up and put down in a new family.
His reaction and response are completely consistent with his life experience. He gets moved about at whim, “family” come and go and he finds himself in a new place, with new people, who expect new things from him. If he can’t do what’s required of him, he gets moved again. The safest thing for him psychologically and emotionally is to treat this like another foster placement because then he won’t be disappointed quite so much when it comes to an end, and subconsciously he’ll push you to end it because as hard as it is, that’s what’s familiar to him. I imagine the idea of someone loving him unconditionally, forever, is absolutely bloody terrifying.
This is going to take time, commitment, consistency - there are literally no short cuts, his whole life has been a cycle of disrupted relationships and moves. You’re going to need to show him day by day that you’re not going anywhere - even if he thinks you will. Life story work will help, but it’s not a magic bullet. I’d start now looking at attachment based therapies, we’re doing DDP with our daughter who was placed at a similar age and has attachment difficulties. It’s based on Dan hughes work on therapeutic parenting so fits well with our parenting approach, we’re doing it through CAMHS, it takes a full history of the child, you and your partners attachment style and looks at the dynamic between you and your child before then doing joint and individual work with you all.
I’d also suggest you both really attending to your self care, make sure you both get time out, cover the eating, sleeping, exercise bases properly, if you’re not already in therapy, get a therapist - someone who will be non-directive and will give you space to fill up again emotionally. The answer to this is going to come from long term, consistent love and care - professionals can help but the day by day work belongs to you. The rejection stuff really is him keeping himself safe by holding you back, it’s not personal (though it feels deeply personal) - my DD will still say she wants to go back to fosters, she doesn’t love me, she wants to leave. It’s become much less over time but I remember how stinging it was to be knocking yourself out to care for a child who said they preferred someone else. I know it comes from a place of fear, now, and it washes over me to where we can laugh about it sometimes.
Reread books like Building Bonds of Attachment to remind yourself why he is the way he is, it’s a perfectly normal survival response, albeit not conducive to family life.
What is the psychologist suggesting in terms of your parenting of him? The whole “social chameleon” thing is fine to say, but what are they saying about how you help him have a stronger sense of self?
Are there specific behaviours or situations you’re finding tough or is it the whole thing? Remember you’re still early days - you’ve only been a mum for 6 months, in usual circumstances your child wouldn’t hardly be mobile at this stage, much less telling you they aren’t yours. Be realistic about what you can expect from you and your son, you’re working against 7 years of history with 6 months experience, it’s going to take time.