I'm not familiar with the 6H23 (I use EH 6922s, which are what my 3iX came with, but I don't think they are the thing if you have "hot" tweeters). You might want to talk to Kevin Deal about mellower tubes in the 6922 family. The Genelex Gold Lions were actually a bit too stuffy in my system, but otherwise had a very nice tone and dimensionality.
Also you simply may need to damp the room even more.
Also you simply may need to damp the room even more.