It's definitely worth to take a look at the faculty of the Ivies too, and see if there is a good fit in any of them. They tend to have very good professors in both US and British history, as well in gender things -although with different focus, depending on the place-, so I'd at least explore their faculty webpages and the titles of past dissertations if they are available.
Because of your interests in culture, media, sexuality, etc. it might also be a good idea to consider American Studies Departments. They tend to be especially interested in these kinds of topics, and I know for a fact that people in American Studies PhD programs work on projects that sometimes don't even relate to the United States, so your transnational or comparative US/Britain idea could perfectly work. From what I've seen, American Studies departments tend to be more heavy on theory and less committed to methodology and archival work, so that's something to consider.
Also, I've seen people in English Departments do interesting work about the history of media, so you might want to look at these as well. Now that's of course a whole different beast (while there are differences between Am. Studies and History, courses are often crosslisted and a degree in one could very well land you a job in the other department, depending on your research), so if you are committed to being trained as a historian you might not like it that much.