I feel you, man.
I would suggest a different path, though.
Rather than applying to another institution, how about quitting your PhD program at your current institution with a master's degree?
I thought in the US, there are many programs that offer MS/MA en route to PhD, i.e. after you get all your credits from courses. Usually in 1-2 years.
Since the objective is now to get a Masters, who your supervisor is for these two years won't be as significant as if you're aiming for a doctorate.
You still need to write a MS thesis under the lab's research area and this new area might not excite you, but I think it is an acceptable way out.
Who knows, after 2 years, the new area might be your favorite area and then you can just continue on. If it doesn't work out, you quit with your masters.