Good idea. In the current case, we don’t need to defeat the best attackers. We just need to render ineffective an appliance deployed by a greedy/intrusive ISP.
So, we don’t need to completely eliminate any signal via CBR. We just need to disguise it enough to confuse an automated system.
Something like a VPN tunnel that padded requests and responses with variable amounts of random data (that could be discarded at the endpoints of the tunnel) would probably defeat most automated attempts at monitoring.
And it would be fairly cost effective. I wonder if any VPN technologies already do this?