Boss,
Scottsdale FSDO have changed the rules slightly since you were last there. Don't bother going all the way to Scottsdale, because they won't issue you with the license you need. Instead, they'll give you a list of phone-numbers of the examiners. You can save yourself a journey by either calling the FSDO for this list, or get it from your flying club. You then need to pick a name and phone number at random, call that number, and arrange to visit the examiner in his home.
The "examination" will basically involve checking your UK license and medical is in order, and that you can speak English, and then issueing you with your US license, for a small fee.
No big deal, just a bit of formality and a way of taking money off you before you even get to fly.
FFF. .---------
PS This only applies to Scottsdale - each FSDO makes up their own rules. Anyone flying in another part of the States will need to check the local rules - it may be appropriate to visit the FSDO in other areas.