"Christ's isn't going to convert to academy status so it wouldn't be in a MAT"
Not unilaterally, but if the CE Diocese was to coordinate the formation of a MAT (like the RC Diocese has done), then I wouldn't be surprised if they looked at it again.
"but very few come from Middlesex as foundation places are undersubscribed"
Christs' historic under-subscription isn't widely known about, and I suspect that if those places are still under-subscribed (anyone know for 2014?) they won't be for long now that the linked school policy has been dropped and people are finding it harder to get into other secondaries.
Also their foundation-place policy used to prioritise certain parishes on the Surrey side of the borough, and still now has a distance element to it, which disadvantages families in the south of the Borough.
"However, as you say Archdeacon C and St Mary's and St Peter's have access to Bishop Wand, as well as StRR, Twyford and the Green School , and many are choosing selective privates too"
The numbers doing that have increased since the linked-school policy was dropped - for the most part families are putting those schools as lower preference to Teddington/Orleans Park/Waldegrave (although of course not in all cases). A good/outstanding local community school will generally be more popular than a commute to a distant faith school of similar quality, even for families at CE primaries.
"is the 'mixed secondary school' that TH's admissions point was too close to Twickenham Academy?"
This consultation question made that clear: "We propose moving the admissions point to another location more equally distant from other mixed schools in the vicinity.(The current point is located much closer to Twickenham Academy than to any of the other mixed schools in the west of the Borough). Do you agree with this relocation of the admissions point?"
"And is the 'new free school' it might be close to REEC or Kingston Academy?"
I didn't say it was close to a new free school. The 2015 admissions point was constructed using a method that will be undermined by the creation of a fifth community secondary on the Middlesex side of the borough. The new point is independent of the location of any new secondaries, unless they happen to be closer than 2237m, which is unlikely in the foreseeable future.
"On the other hand, a catchment isn't always a perfect circle around a centre point."
Exactly. Given the popularity of Teddington I wouldn't expect its catchment to be much impacted by TH's admissions point (or the establishment of KA for that matter). And given the location of Bushy Park, TH's catchment is very unlikely to be circular. That is why the consultation report says: "Both the current admissions point and the new proposed one serve the original, existing and future area of demand".