Artimuse, I'd had both problems in the past. For the falling asleep, I don't worry about it. Just like Shawn suggested. Master Lin says that sleep is when we naturally go into the emptiness. So no harm done, right.
However, falling asleep is not the same as my other experiences of drifting into the emptiness while doing the Small Universe. So the best thing to do is get more sleep. It works for me.
As for the sore back, I looked on it in a few ways. One my muscles need to become stronger. The other as a message that my position is not quite right. So I take a little time correcting my posture. I've tried leaning forward, and backwards a little to find the vertical. Tucked that chin in. Imaged a string pulling the top (wisdom tien) of my head up. Imagine my back pressing against a wall. Move the position of my hands on my lap.
It eventually went away..... good luck.
Play with your position a little, but then let it go, and get back into the meditation. Eventually things will go from good to better.
You are perfection.
Iam2