"The only other possible reference to a Michael COURCHER (and variants) I have found in any searches is
Michel COURCHE b.5 Jun 1752; chr.28 June 1752
La Patente French
Huguenot, Spitalfields to Jean COURCHE and Marianne
AUDRY.
Possibly Anne COURCHE b.1 May 1754; chr.19 May 1754
La Patente French
Huguenot, Spitalfields to Jean COURCHE and Marie Ann GAUDRI is his sister."
This clearly goes back to the IGI: John Courchee and Mary Anne Odree married 16 APR 1748 at St. Matthews, Bethnal Green (extracted). Besides the obvious spelling variation, there are also changes in location. The LDS library shows the parish registers for Bethnal Green begin in 1745, so you're there already. The Spitalfields listings certainly have to be considered as another fairly good indicator of
Huguenot ancestry.
The John versus Charles question is more likely resolved by the actual name being John Charles. It is quite common to find that various
Johns,
Jeans and
Johanns are sometimes recorded by their middle names. And as you say, it appears that any twin was not recorded with his birth sibling.
Your investigation is definitely in a phase where the database is expanding and you should contunue on this path as far as you are able. You might also see what you can find for some of the death listings of the more significant individuals. The possible inclusion of 'incidental information' can be very important for an investigation and you really can't predict where it might occur. As people moved about, sometimes it was recorded where they were from. Such indicators may provide some significant information.