You can check with the department to see what scholarships are available to American students. The route around "citizenship" is permanent residency, but you can really only get that if you lived there for more than 4 years, and working full-time, not as a student. Or if your parents work there and you are in the country as a dependent.
The difficulty with American tuition is that they charge you more to begin with, and a lot of the scholarships available only cover British tuition. You also can't apply for AHRC funding.
There are a number scholarships available from American organizations however, you'll just have to look harder to find them.