I too had initial difficulties and frustration. I developed a technique that works for me. The first thing I do is lock the orientation. Then I put the left edge on a desk or table. Now I've got a firm stable consistent edge to work with. Now I find it considerably more consistent to be able to press both buttons at exactly the same time.
Nexus 7 (2013)
Signed up for the expressed purpose of saying thanks.
I was having a devil of a time getting my legacy nexus 7 to take a screenie and while I didn't have to lock the orientation, stabilizing it on a table did the trick.
Thanks again.