further to Anevilgiraffe's idea, I'd use pegboard (perforated hardboard) for the base. It's readily available at DIY stores in precut sections 4'x4', they will cut it to size for you, just needs a good slap of paint and draw your grid lines on. As it is pre-holed, little work, holes are accurately spaced, all that would be needed is pegs; also readily available (roofing nails or shelf hanging pegs). Players place the peg where they move and add the string. You might have to add a spacer underneath (insulation foam). Come to think of it I have a spare piece of pegboard...