The only aspect of relevance in terms of the FAR's is a student going solo.
And how is exactly is a student going solo in an N reg aircraft in US airspace then? They can't be doing under your licence as a JAA Instructor as you don't have the right to send someone solo in a foreign registered aircraft and as you are not an FAA CFI you can't do it.
The only way it can be done is on a FAA student pilot certificate.
Which means that student must then have the minimum required training with an FAA CFI..........