It might be that by dipping your right shoulder while looking over your left applies counter pressure to you handle bars and causes you to keep the bars and bike in a straighter line. Just my 2¢ (although, not for much longer, the Canadian Mint is no longer producing pennies so thoughts from Canadians will be much more expensive).

"Most" cars tend to use daytime running headlights so my first glance is a very quick slight glance to look for headlights and if I see none, I will take a bigger look with more rotation and for a longer period. Doesn't always work but since my morning commutes are between 6 and 7am, traffic is generally light, the sun isn't fully up (at least, not at the start of the commute) so I can generally count on this technique. On the way home, I will tend to "ride safer" and pull to the curb and stop if I really need a full look. I also listen for the sounds of tires which is very important for me and will give me a measure of confidence that if I hear no tires, I can more confidently turn for a look.