OD,
No problem with any of that, except for the fact that I don't see what is stopping the US company registering for VAT in the uk. If it owns the aircraft, and carries on a VATable activity (which will depend on the circumstances of each case), then it can registrar in the UK for VAT.
In my example above of the two companies renting out planes to PPL's, it wouldn't make any difference to the VAT position if one of the companies was registered in the US (or Uzbeckistan for that matter), and the other in the UK. It's the place of supply of the VATable activity that counts, and not the place of registration of the company.
Of course this is assuming that the US company is carrying on a VATable activity in the UK.
Anyway, the point of my first post on this topic was to point out to the thread starter that he needs to consider the VAT with a professional advisor. In all likelyhood with will have to pay the VAT either on import or on the hourly rate, and it will add 17.5% to his budgets; not an insignificant sum.