"I began shaping, picking up a stitch at each end of the neck with each row - when all the way to the end and ended up with a giant collar very unlike the photo. I am wondering if I am supposed to add 2 stitches at each end?"
Instead of one stitch at each end, you should be picking up 2 more sts from the resting sts at one end and adding them to the worked sts. This is what the pattern is calling for and it will work into the k2p2 rib more neatly.
That's not going to change the number of rows that it takes to incorporate all the required sts (one stitch at each end per row or two sts at one end).