I've been using a Baron for the last six months with my CLS1's -- I particularly like it's adjustability (i.e. tube options are 5881/6L6's, EL34's, KT90's, KT99's), four settings for negative feedback, tube adjustments). I initially adjusted the tubes (various combinations of pentode/triode) for source material but also liked the flexibilty when playing with IC's. I've got things pretty much "dialed in" right now so I've settled on two-thirds triode and zero negative feedback. With the right associated equipment this is a very nice real world amp, especially for the money. I listened to other amps with more finesse, but at the time I was running the CLS's by themselves and the ability to adjust and zero in on the best sound won out. Now that I've added the Kinergetics SW800 subs run by a separate amp, I might consider other tube amps to run the panels. (Adding the Kinergetics brings CLS performance up to a completely new standard. Just amazing.)
I have had feedback from another member, however, who had problems with the Baron driving CLS II's. I don't know whether they were z's or not, which I think would make a difference. I think it's definitely worth a listen since your dealer is local -- maybe a demo in your system. The tri-tube upgrade is a big plus. If you pull the bottom panel you will see a note as to whether the upgrade has been performed. Good luck.
