Hi
Firstly as another parent who lived overseas are you entirely sure that your son's social skills are to blame for his social difficulties. Both my daughters found the different culture hard to adapt to after an International School . In particular DD2 who is gregarious and friendly found coming into a Richmond Prep (and if the school your son is at is the one I am thinking of, it is effectively a Richmond Prep) incredibly difficult even in Year 4, it was already very cliquey and exclusive and, shall we say, with little diversity. She was also told she was annoying, and too wild. Her class teacher said she thought that perhaps the girls concerned needed to learn about opening up as much as she needed to restrain herself! It must be even harder in Year 6. They still have friendship groups that are largely comprised of other children who have lived in or whose families come from different cultures, and really can't tolerate the values and exclusive behaviour of the "cool kids".
The selectives love students who have been overseas, really value the benefit of their experiences and let them know it is valued. I know they take it into account in assessing academic achievement in exams.
Don't know all the schools you list as they are rather geographically dispersed and this is of course subjective but DDs are now almost through school so I have direct and indirect experience of some.
KCS has it's fair share of cool boys but I also know "nerds"and "eccentrics" who have done well and been happy there. Quite a few from other cultures too. Very good teaching and results and competitive to get in. IB in the longer term, which is good internationally, but a high workload (though it gives you lots more scope to increase points), and both DDs were glad to specialise for A level . All the selectives we applied for cut off in October / November, would be surprised if they narrowed it down by an early cut off which will tend to favour parents in the know, which isn't so much of an issue when they are applying from Preps at 13 .
KGS has a new head and a real buzz at the moment. I don't know anyone who has gone there and not been happy. They seem to be good at creating an environment in which bullying is not regarded as acceptable by the pupils as well as the school which can't be said everywhere. Not as good results as KCS but I think we can get a bit picky about whether the selectives around here are in the top 10 or top 50 when both would be regarded as very good in the rest of the country and enable bright pupils to get As . But will girls, especially hormonal ones add to your son's shyness? From a girl point of view I think the presence of the other sex cuts the bullying. Also the sports are in Thames Ditton which is a long way if he develops a talent for Hockey or rowing, and I think most pupils are quite local. I would definitely put the journey into your equation, an hour or more at each end of the day is tiring .
Ibstock used to be for the arty and sporty who didn't want an academic hothouse, and was popular with families coming back from overseas but now has decided it wants to be academic as well. I think that has involved a fair amount of close supervision and intensive teaching to improve results, which has created some tension amongst those who signed up for something different, especially as there has been some effective exclusion of pupils who did not, or could not, buckle down. However that may have worked its way through in as much those joining now know what they have signed on for. Also it can be cliquey, not as diverse as some other selective schools.
Christs was a disaster area, nearly closed but was reinvigorated by a new regime but it has been a bit of an uphill battle to change perceptions as well as results and it is still not oversubscribed . Richmond Park Academy nearly matched it's results this year (Christs 93 5A-C, 73% incl.Maths and English , RPA 91%, 61%)Sounds as if the Head at RPA is achieving exciting things. Both schools about to get sixth forms, the lack of which I know has been a put off for some.
Overall though I would recommend you narrow down your list and visit, there is no substitute for going around a school and getting a feel for whether it is right for your child .