the confusion came from the difference of Fair Ilse knitting and intarsia. I thought you were doing intarsia(every field of color has its own ball of yarn, nothing is carried) and really you are doing Fair Ilse or stranded knitting.
I am currently doing a lot of stranded knitting and here is how I do it:
My blog with video link
If you are able to knit Continental as well as English Style, the Philosopher's wool video will help you a lot, as well!
Congrats on turning the heel!