I went with root and rowter because you didn't have a choice for root/rowt and rowter. Like Karen, whether I pronounce route as root or as rowt depends entirely on the person I'm talking to. That leads me to believe that my parents' Oklahoman accent keeps slipping out of my mouth at odd moments, as does the Colorado accent I grew up with. After all, I still vaccilate between pilluh and pillow.
I also went to the link you posted and listened to the pronunciation. I don't know if you realize it or not, but the speaker had an English accent: ROO-tah. Not only do most Americans pronounce the first vowel as an "ow," but the second syllable is almost swallowed up in the growl of the final "r." So both syllables are completely different from the English pronunciation.
