The confusion has to do with knitting in the round and doing and intarsia-type stripe, right? I'm not positive about this, but couldn't you do the stripe continuously, like a barber shop pole, or a candy cane? If the stripe is only one or a few sts across, you would have very small or no floats. Otherwise you would have to cut the yarn.
If this isn't what you were getting at, post a picture of the scarf you want to copy.
Hope that helps!