I’m a nocturnal animal and its tough not being able to run most of my tools in my garage late at night when I prefer to work. I found this, http://www.instructables.com/id/Soundproof-Your-Garage-Walls-Using-My-Cleat-Meth/ , while trying to figure out how to keep the noise down in the backyard shop I’m planning while not breaking the bank or over complicating it. I may be mistaken but from what I understand it’s a similar concept to the resilient channel that X-CNC mentioned.
While it seems to be the best bet for me since I’m building from scratch, as I plan on just running all of the electrical in conduit and dust collection tied into the cleats. I’m not sure how well it would work in your situation with the garage, outlets, and whatnot already in place. Obviously I don’t know your budget or how big you want to go to tackle this, but there is always the option we used when I use to build high end home theaters of building another room within your room. You could build these cleat type walls over the existing walls of the alcove and then add a front wall. Or maybe just build a small “room” out of some heavy packing blankets to take the edge off.
Maybe we are trying to kill a mosquito with a shotgun here though. I would definitely try to minimize the the source of the sound. Like Mike and Benjamin said, it could be the vibrations resonating through the machine/table/etc and amplifying it. Is it equally loud when cutting flat stock secured to the bed? I can run mine with the garage door open in the evening when it’s fairly quite outside and its barely noticeable 20 meters away at the end of my driveway. My shop vac with the silencer in is still the loudest part of the setup.
I’m curious what you figure out and what solution you come up with.
On a side note, I’m in the middle of upgrading my machine, and had been contemplating an almost identical setup to yours with the rotary device. I think you pushed it over the top and I’m gonna bite the bullet on it.