A down spiral carbide bit will make a big difference. It needs to be very sharp for best results. Sometimes a layer of painters tape over the area to be cut will help to hold down the edge grain as it's cut. Slightly dampening the surface veneer in the area to be cut also helps. When all else fails, scoring the cut lines down through the veneer with a very sharp knife before removing any material with the router will help. One or a combination of these should solve your problem. I usually try them in the order posted until I get the results that I need.