pick up teh bike
Here is how they taught me to do it at the BMW off-road course. (on a F650GS)
Grab the handle bars on the ground side, turn the front wheel so that it is upward to the max possible.
When this is done, face the bike and squat a bit (don't break your back!), pull the handle bar up (the one closest to the ground) so that the back wheel is now resting in the ground as well as the front one. Make sure you are in gear (if possible!). Then, still grabbing the handle bar closest to the ground, and the 2 wheels touching the ground, push the handle bar down and then then up 1 or 2 times. Somehow, the bike will "pop up" high enough so that you can use your hip and leg to continue to pull it up.
It sounds complicated to explain, sorry! But it works, I did managed to pick the bike up on my own.
I did try to squat once as you described, but I had the same problem than you, the bike lay down completely on its side and is too low for that.