Hi Folkfan: I may try a possum board at some point - I have a small lap so keeping my dulcimer from tipping when I play near the "ends" has been an issue in addition to the slipping, (I had tipping problems even with the shelf liner), so a strap is probably my best solution.
My possum board has shelf liner glued to the back of it. The lifts that hold the dulcimer up off the board are shaped like shallow L's and the part that touches the dulcimer back are felt lined. No scratches, no slides, no sticking to the board. And I can angle my legs comfortably. Plus in case of extreme need, one of my possum boards has strap buttons. How's that for covering all bases.