Dirty harry,
You are correct, but what is the point of what you are saying because the required courses at all US airlines are the full ATP and Type rating given under the company umbrella, so you would still have to do the same amount of work.
After the Eastern Strike and the hiring of unqualified replacements in "short courses" there are NO SHORT COURSES ANYWHERE IN THE US. IF I get out of the cockpit of a 737 for airline x, I must still go through the ENTIRE program for airline y as a US citizen flying for a US airline. What you are asking for is a shortcut simply because you are a foreigner, that is not available to any US citizen. The license is really irrelevant because you cannot use it without completing the company courses unless you are looking to again exchange it with another country that doesn't take your British License. That is a practice that is also decried.
Cheers
Wino