Prader Willi wouldn't seem likely - that's usually very obvious from an early age - the overeating is really quite extreme & constant, & most commonly IQ <=70.
I was really very overweight as a teenager (size 18) - comfort eating & lack of confidence at sport, & my brother was also quite tubby (he lost it all getting taller, & now he is at uni & lives on pot noodles he comes back worryingly skinny sometimes).
I wouldn't dismiss family therapy 'till you've tried it - my family had it for a while (when I was in hospital with ED) and it was actually quite helpful - I suspect with all of us having some level of communication impairment &/or mental health problems it was useful to have a while to talk with someone around to look at what we were doing.
Hope the ed. psych is useful - i'd expect them to know a fair bit about dyspraxia, it's probably one of the commoner things they'll deal with.
[important note: I don't claim to be 'expert' on anything. I'm a psychology undergrad, which in no way qualifies me to do anything, and I have dyspraxia & lots of my family have dyspraxia or other PDDs].