ETOPS - believe it or not, no matter what letters you have - and no matter who wrote it/them - the final decision on your entry to the USA is the litttle man behind the desk at the airport of arrival.
Even with a personal letter from the head of Immigration, if the little man doesn't want to let you in - you do not get in (so don't p**s him off with any attitude or argument).
Just turn up with a visa and be straight with him.
Even with a green card - I am still at the mercy of each individual immigration man on the daY I walk through!!