Cameron -- you can't pull it. You can't even dig it. If you do either one, it just grows multiple starts from the point where the root came apart. It's enthusiasm is unparalleled.
To get rid of it, especially where it is seriously entrenched, you have to spray it -- with a grass killer. And one application likely isn't going to be enough -- two or three or four applications, depending on the severity of the invasion. I sprayed mine once last year and caused a set-back -- I'm going to tackle it with a vengeance this year.
Anyway -- I'm glad you like Pompano Peach -- I hope I can send you some.