I decided that I need to do something about this otherwise I just won't be able to get much done, so I started to see if I can put some kind of dust collector into the router table. Most plans show a dust collector connected to the back or base of the router, but a lot of people also mentioned that this didn't work very well in actually capturing the dust. Also, a lot of dust actually accumulate above the table.. Buying a Festool 1400 and the CMS module isn't a realistic option, so I did some more searching and found the Keen Dust Collector for Routers.
Essentially this is a little rubber cut that you put on the underside of your router plate so that dust doesn't fall down into the router and router table. By limiting the space where dust can spew a vacuum's section is a lot more effective in capture the dust.
I have a Bench Dog 40-001 ProTop Contractor Benchtop Router Table which is an enclosed router table so setup involved drilling a hole in the back to run the vacuum hose through.
There is is plastic sheet that sits between the router base and the router table. It has a velcro ring that the blue rubber cup sticks to so the cup doesn't move around. Mount your router and put in the rubber cup and then attach the hose.
Conclusion? It works very well! I cut multiple dados through 3/4 in plywood and very few dust got on the floor or into the router cabinet. It was good enough that I felt comfortable going right back into the house after a slight dust off with my hands for some dust that did get on to my shirt and pants. For about $40, you can have a pretty effective dust collector for the router table that can save hours of clean up.