I have CLS IIz's and have a bit of a different take on this...
First off, Congratulations on buying CLS'!!!!
I have been known to play my CLS's at a pretty aggressive volume and with very dynamic music, so I was especially sensitive to the swaying of the panels. The CLS's are not at all rigid and the louder they play, the more image smear you get. The reason I mention this is because I am using Sound Anchor stands. This means that there is absolutely no swaying but unfortunately it also means that there is no floor-coupling, so audible bass output is even lower than what you are experiencing.
Also, as I mentioned before, I tend to prefer listening to music (mainly rock) at "realistic" levels :rocker: , so this poses another problem for the CLS'. They do not like to play loud in the bass region without the bass panels "pharting". So, I do not run the CLS' full range, I cross them over at 80hz, to two Depth's; one behind each CLS. The integration is outstanding, I can play my system at frightening levels without worry (it pays to have an amp with the cojones at 2 ohms or less), and I get very tuneful, well-integrated bass.
I came upon this combination after trying the same crossover scheme with a single Depth, then later, a single Descent, then finally 2-Depths.
The Depths have amazing flexibility in tuning and with patience and care can reward you with superb integration with the CLS.
See my system pics.
Oh, by the way, Tweeter is getting set to close most of the old Sound Advice stores in Florida, so ML stuff in stock will be aggressively discounted!
Good Luck,