I can see why you feel the CJ isn't quite up the what these speakers require. I had a similar experience/problem and here's how I solved it. Don't get me wrong, I love CJ gear and use a CA200 amp to drive CS2.4s in a second system.
A Krell FPB 400cx (KCT preamp) is what I've been using since 2003 to power my CS6s, this was an upgrade from Bryston 7BST monos. This amp fully controls the CS6 and over the years the bass extension and clarity have so greatly improved that any thoughts I might have had about a sub are now long gone. And over the yers, I believe the amp finished the break-in process of the speakers so that they could fully perform. Also, the mids and highs are sweet and three dimensional' it's hard to imagine improving this, perhaps with a 700cx or their monoblock versions. With this setup there is little, if any, in the way of current limitation from the amp and with the excellent dynamic range afforded by the Krell cx amp, this is what these speakers require to work optimally. Beware: I also in home demoed a 300cx before deciding on the 400cx; the 300cx simply didn't quite have enough juice for the CS6s and the 400cx made a noticeable difference, so for me, it's a minimally required level of amplification for these speakers. Levinson (300 series) and Pass also work well. You do want amps that double power as impedance halves, at least down to 2 Ohms.
