Can't say I've worked with polyurethane but I've done a fair amount of sound dampening. I would imagine most of it comes from the router, the rest comes from the router transferring vibration to the frame of your machine. Sound is vibrating air. Stop the vibrations, stop the sound.
What's your machine made out of?
To quiet the large compressor in my shop I wrapped the tank with 2 layers of roofing bituthene, then built an enclosure around it out of MDF,bituthene and egg crate foam. I used lots of screws, bracing, wood glue and caulk to seal that puppy and make it impermeable to vibration. (I used to build custom car audio, and probably will again once my machine is built)
Mass is your friend when it comes to sound dampening, do everything possible to securely attach the router to as much mass as possible.
It sounds like a great idea. If only you could plug those darn vent holes in the router.
Post some pics once it's done.:banana:
"I've got a long way to go and a short time to get there, We're gonna do what they say can't be done."