I don't understand what's wrong with your guys' Eco Vues. The strap on mine holds the iPad so well in the case, that it was even a little hard to get it out when I put my SGP AF screen protector on it yesterday.
Can I ask how long you've had yours?
I have a feeling it's an age thing. I've had mine for 2 weeks now. At first the strap held it quite well and overall the whole case was pretty tight. But the leather stretches. It's pretty loose now and I can slide the iPad from side to side (portrait) about a 1/4 of an inch. But back to the strap, it's starting to slip out just by moving the case around. I constantly have to push it back in. And yes when flipped upside down or anywhere near, the iPad slides right out.
I'm thinking that a small patch of velcro near where the strap and the back cover meet but closer to the top of the case. That way you can still reach it to break it free and pull the iPad out.
That or put some more magnets in there to hold the strap in, lol.