I have ongoing bowel problems & my husband has had a large part of his removed due to it being pre-cancerous. Anyway, I bought an Australian book recently called "Happiness is a Regular Complete Bowel Motion!" Amazing what you can find at the bookstore! This book gives lots of information on squatting in the bathroom and gives a couple of websites: www.naturesplatform.com and www.mypage.tsn.cc/self-helpconcepts/. These argue strongly for the benefits of squatting.
I have the same experience as you with the leaning to the left, maybe I have some congestion there that requires extra pressure to get a bowel movement past.