Tube rolling on Leven CS 600

Interesting. 
I had the 600 with Devore O/93s. After running various EL34s, GL KT77, KT90, 5881, and the Russian equivalents Jeff Day popularized, I eventually settled on GL KT66, which I found to be the most balanced.
I'm usually not one to put much weight on the notion that cables can transform a system, but: which cables are you using? I find that the apes like being fed with A23 wire.
All that said: the Leben is not a "tubey" amp and in my experience no amount of tube rolling changed that. (Nor experiments with footers, dampers, and incantations.) If your streamer follows the traditional Linn house sound, then it majors on fast and "clean"; I've also found the Feikerts I have (briefly) heard to be somewhat in that direction. Probably not what you want to hear, but them's my 2 cents.

I usually ran the CS600 with the lid off, but I recall -- I haven't had it for a few years now -- that the GL KT66 were able to fit below the lid. 
The upstream components don't look to be at fault. I've only heard one system with the Luna cables and it certainly didn't have a harsh sound; based on the company (dealers) they keep, they seem very compatible with the Leben and Devore. That leaves two things: your cables and the room. Can you experiment with, say, some Luna cables and changing speaker position, at least temporarily?