The MKII they brought in Shelby, though how much he and his shop were involved I don't know. But it was Shelby who wanted the 427 put in the car and a transmission to back it up.
The MKIII was the road car for homologation purposes.
And as you said MKIV was almost entirely American (still had most of the old body work).
I'm wading a little out of my depth here (American car history isn't my speciality), but wasn't the MkII (GT-40 that is) still in the UK during development? And as I understand it, MkIII's are usually ignored since they were never racing cars and largely irrelevant (at least among most fans, as far as I can tell).