I'm trying to figure out what you're wanting to know. Do you have w&t stitches right next to each other? I've always had stitches between the turns for the short rows, but if you don't I guess that could make a difference. By first wrap around stick, do you mean the stitch on the needle and the wrap? Maybe a picture would help clarify. IME all wrapped knit stitches would be picked up the same way.
This is the last time I'm frogging this project for the last time.