But as some anecdotal advice: a friend applied to the PhD program at UVa a few years ago without taking or submitting subject test scores. The department told them that they could submit the scores if they were offered admission -- which means for you that you could potentially take the test once you get to the US and begin the program -- although even after enrolling and completing their degree, they never bothered to take the test or submit the scores and was never offered any grief about it.
I'll bet that if you emailed the DGS or department secretary, they'll be willing to work with you so that you can still apply.
I had two different bookmark folders: one that contained the links to the English Department website for each program and one with links to the application itself. That probably saved literally hours of searching over the course of six months.