I am new to this forum but I have always knitted what is called "combined" method. It should work fine for k p ribbing without stitches twisting. But I don't understand why you are wrapping when you purl. I just go through the front of the stitch and hold your yarn in front of the left hand needle and pull it through with your right hand needle. use your left index finger finger for tension. As for knit stitches go through the back loop and pick up the yarn with the right needle.
Maybe I don't understand your quesion.