It is not really a grey area - I think you are trying to make it so.
You are coming to the US for flight training leading to a certificate/rating. You need TSA and officially need a M1 visa and hence require a Part 141 and SEVIS approved school.
At the end of the day it is entirely up to you if you choose to go some other route.
Did you read this link further up this thread?
http://www.pprune.org/professional-p...ml#post6841179
The fact that you have done some training in the UK is irrelevant and presumably that training was not done with a FAA Authorized Instructor (as defined in FAR 61.1) because officially you should have got TSA clearance before starting any FAA related training - even if it is undertaken outside the US.
You need to review 61.65 to determine how much training you need to complete with the FAA Authorized Instructor as some of what you have done may not qualify.
What are the longer term intentions of the FAA IR? Are you planning to go on to Commercial etc with the view to trying to work in the US?