How close are the bypass caps to the actual chip? The inductance and resistance of PCB traces will affect how effective they are. The 0.1uF should be as close as possible across the pins to ground. If they aren't try a 0.1uF or even a 10nF straight across the pins.

The brute force approach of 1000uF on 3.3V shows you're probably on the right track. I'd try some smaller ceramics instead since the electrolytic (I'm assuming you've used) will have a high ESR. Some 1uF or 10uF decent ceramic caps are likely to help more IMO than your big electro.

A good high speed CRO might catch something on the supply lines but I'm guessing you won't have that. Stick with the filtering.

Got any ferrites? Try running a few turns of the of the CBUS lines. Might stop the ugliness getting in. One thing I've found with EMI/EMC is that often once the noise/interference gets in, it can be hard to get it out, so try and stop it at the "border".