This is interesting. Please remember that I must make the system unobtrusive. The players, as much as possible, should not have to change their behavior. They will not look at the computer screen, and cannot have their view of the board/pieces obstructed at all. Many of the players are just starting out, young kids, and I don't want to confuse them by giving them a different experience than when playing over the board. Only when the game is over would I direct their attention to the computer screen as we go over the game.
I think your experiments prove that the coverage of LM is, at best, 10" on either side of the unit. Thus putting the LM (even on a small tripod) somewhere to the side of a 20" board (where it cannot be knocked accidentally by a player) does not seem feasible. I guess the coverage is just not there. Thanks for your input -- it was very helpful.
BTW, I looked at the Kinect SDK. The unit is much more expensive, but would work nicely if it were not for its size (it is too big). If LM were to provide the same interface (Kinect delivers all objects in its view) and/or increase the LM coverage, it would support many more applications. They might add a standard tripod screw while they are at it.