Hi - I have had a similar problem. I am absolutely convinced that the problem is far more to do with the table than with the router. The table can act as a loudspeaker, capable of vibrating at its own resonant frequency (or frequencies) and effectively amplifying the sound the router/cutter makes. The frequency range is generally mid-spectrum and does penetrate very effectively. I bet your router when handheld is far far quieter??
If this table was mine, I would add mass (weight) and damping (anything soggy) - add a sheet under, well bonded to the main top (with aperture for router and mount of course). I am about to make a new one and plan to use one layer of cement sheet (sorry don't know the tech name) in the table-top sandwich. It's in most diy stores - try a sheet of that, bonded with a roof repair medium (bitumen) and compressed tight. So a layer of the cement sheet, 6mm mdf or ply (prefer ply) under - bitumen between all 3 layers (table underside, cement, ply) then clamp tight for a few days to let the bitumen go off. That is just patience, and a flat surface and plenty of weight.
Otherwise just add say 12mm ply under, but bond it with an 'elastic' medium (Bostik, Thixofix etc) - at higher frequency the shearing between the materials will dissipate a lot of sound energy.
Personally, I am actually excited about the cement sandwich approach - will definitely be on my new router top (with a really stiff flat top surface, of course!)
Sorry this sounds odd and Heath Robinson, but combining stiffness with mass will make a big difference, as the vibrational energy produced will be dissipated into the structure, whereas at the moment it is 'driving' the top like a speaker.
(sorry, a one-time acoustics engineer speaking)