6stsx3needles=18sts to start
row1: 18/3sts per repeat (k2tog, k1)=6groupsx2=12sts
Nope. Seems to me you can end with 8 or 5 but not 6 and therefore you cannot have 2sts per needle.
I guess on row 3 you could omit one k2tog to leave the extra st and end with 6.