projector causing flicker

My game pieces and board spaces all have "iphone/lightmap/lightmap only" materials with white lightmaps. I'm projecting a large mood lighting shadow over the board. When the pieces are sitting on the spaces there is a flicker on the space material, but not the piece material. If the piece is moved to another position, that new space will flicker and the previous one will stop flickering.

It doesn't matter if I use a highlight or multiply projector. It stops flickering when my overhead camera stops moving, but the artifacts of the flicking are usually still on the spaces. A static camera that doesn't move doesn't cause any flickering.

The flickering is the worse at the outside edges of the board. That may be because the camera always looks at the center of the board as it tilts to follow the iPad tilt.

I've got other shadow projectors with the same shader for casting moving shadows on the pieces and spaces below the floating piece, but those don't cause any flickering.

I extended my camera's near clipping past where it was unusable to see if that would help with z-buffer precision, but it didn't seem to make a difference.

Has anyone run into this problem or have any ideas?