Have u thought of using a swiss ball. I do pilates on my swiss ball so im not on my back to much.
You can lay on your back for a small amount of time, i sometimes does off in this position for maybe 15 minutes or so. The reason they say you cant lay on your back after 21 weeks is because the placenta is so heavy at that point that it pinches a nerve in your spine, as well as cut off a small amount of blood flow, which alot of women find means tingling in the legs, or numbness, and can cause fainting and/or dizziness.So just watch how you are feeling, and if there is any real discomfort, just simply move to a different position :)