Update: I got my hands on a Dehavilland to try out, and it was noisy as well. Luckily, there were some other NOS tubes around to try, so I swapped in a Hytron 6SN7 and, for once, my system is quiet! Wow, does it sound good!
I may just go the Dehavilland route! According to Kara, it mates much better with very sensitive amps such as the McCormack. I am going to get a good SS unit in here to compare it with. The Dehavilland's soundstage is incredible and very realistic, but from what I can hear, the Classe was more taut in the low end. Also, on the Dehavilland, some trumpets come across as screechy: I am not sure if it was recorded this way and I just wasn't hearing it before. I heard slightly more detail on the Classe (like violiin strings reverberating that aren't quite there on the Dehavilland).
Thanks for all of the responses. It gives me something to work with if I do decide to get a solid state unit. I wish I had known about the possible incompatibility with a sensitive amp and a tube preamp before I went preamp hunting: then again, the journey is always fun!