That experience has suggested that this project is not going to be as successful as they would hope. That is because you can't depend on gravity to be stronger than the angular momentum of a router bit hitting a knot in the wood. Specifically when you're routering away and you hit material that pushes back on the router, the router may not move in a gravity planned sort of way. I've seen that in the plotters when the drawing device catches on the material that its drawing on. You get a line that goes horizontal when it should go down.
These sorts of things are pretty easy to pass off when you just hang a new sheet of paper but if it means throwing out a 4x8 sheet of plywood its going to be a bit more painful.
As for discontinuous lines you put a wall sensor on the drawing puck (or the router) and when you need it to move you tell the operator. Who goes over and lifts the pen/router off the paper. The code detects the lift, adjusts to the new position while you lightly hold the puck, and then indicates you should let it back down on the surface. Once the wall sensor activates it goes back to drawing.