There is a Ryan Hall video you can find online that goes through how he finishes and tightens triangles. It shows how you can avoid crossing the arm, and how to get way more power by turning perpendicular. It also explains clearly which muscles you use from different angles (yes, they are different), which should help explain. Essentially, you are more likely to gas yourself or fail, but you can get the choke, no arm across, with your hip flexors (I think that's the muscle that you use to pinch your knees, right?. still, you dont have to be perfectly parallel to switch to stronger muscles. I find a little turn is all I need, especially if I wrap them up by getting under the other side leg or arm. Ryan's ignores pulling the head, but you can combine that in as well pretty obviously for a little extra torque.