Help may be at hand!!
I've just received the following in an e-mail from a colleague in another FSDO...(cut and paste)...
<<The answer is that FAR 61.56 does not state that you must be in a US registered airplane. It just states what must be done as a minimum. So the answer to our Swedish friend is that he can do it in a Swedish airplane just as long as both he and the Instructor are qualified.>>
I'll still be getting the telephone call from Orlando on Monday - but seems that the answer is "Yes".
One word though - the question of "Who would be in command?" was asked by the local team. Don't quite follow the relevance - but they did ask the question.