good luck mate, I've tried a few over the years, the best I've come up with so far is similar to harpz, I have an avid restbite which is a proper lay flat bed and the same as harpz I've tightened the elastics as far as I can and I use a pillow for head support, what I was trying to achieve was my head/neck being in alignment with my spine when i'm lying on my side and for it to be firm with no sagging the no sagging is really important, I even considered trying to put wooden slats under the matress at one point.
if we had a bedchair that didn't rely on an elasticated matress and was solid underneath with no sagging at all and a nice comfy matress on top, I reckon the company that made it would be quids in