"When you're using multiple colors for intarsia, it's best to disconnect them from the balls--you'll get too many tangles."
Take it from me, you dont' want to deal with the tangles.
Something I saw on Knitty Gritty's show about intarsia knitting was creating butterfly bobbins. Basically you wind the yarn around the palm of your hand a few times, and then take it off, turn it sideways and roll the yarn around the band of yarn, so it looks kind of like a butterfly.
Another options is to use very small balls of yarn, so you can unweave them as they get twisted.
I do multicolor knitting all the time, and its just a blast to see your picture come together.