Well, you don't need to use separate needles, just separate balls of yarn.
Work the pattern as specified, but when you are working on the right side of the neck, work from one ball of yarn, when working on the left side of the neck, work from a second ball of yarn. I think you may actually be overthinking it a bit.
Let's say you have to knit 12 stitches on one side of a v-neck then 12 stitches on the other side. You have your yarn attached to the first side, knit across the 12 stitches, then drop the yarn you've been useing. To start the other side of the neck, pick up the other yarn and knit across those twelve stitches. Now both sides of the neck have been worked and the yarn is hanging down off the left side of both sides of the neck.
Turn your work, and start working the side you just finished. Work to the end of that section, drop your yarn, pick up the yarn for the other side and work across that remainder of the stitches.
Does that help?