We just can't get through this wall, and I'm bloody, bruised, and exasperated from beating my head against it.
It doesn't sound to me like you've reached the end of your rope, because you are still there.
Your wants and needs are legitimate, but you are not treating them with respect and neither is she. She is RUNNING this situation with an iron fist, and you are letting her. THAT'S why she doesn't want to have sex with you.
Determine if the sex issue is actually a deal breaker for you. If it is, then ACT like it is. If it isn't, then stop making it out to be because all you are doing is creating strife.
I know you are hoping she will change so YOU don't have to draw a line in the sand. Good luck with that. There are lots and lots of people around here who have done that very thing.
But every single person here is going to tell you, that NOT drawing your line in the sand is the problem.
You also might want to get a book called "No More Mr. Nice Guy." And do the exercises.