I am sure Zybar will be most helpful in answering that question, though he didn't like how the 10" woofer responded to tubes, which is ultimately why he sold the HT3's (I think).
I actually sold the speakers because I found a "better" (although significantly more expensive) product (Vandy 5A's) - not because of how tubes sounded with the HT3's. That being said, the best amp match in my system, to my tastes, was the BAT VK-600SE.
I have no doubt that some tubes amps can do a good job controlling the woofers, but I can't say I had great success. I don't think it is just about the watts, it is about the amp's comfort level driving a lower impedance load and dampening factor, size of room, type of music you listen to, volume you listen at, etc...
Carusoracer mentioned some brands above and out of them, I have owned the Dodd 120's and the McAlister PP-150. I know that the Dodd 120's didn't do it for me, especially when listening at higher volumes. You can read what I thought of the Dodd 120's (the previous, not the current shipping version) in comparison to the Moscode 401HR (hybrid amp) here: http://www.audiocircle.com/index.php?topic=32863.0
As for the PP-150, from the mid's up it would be an excellent match for the HT3's. If your room is on the smaller side and you listen to vocals, small jazz pieces, folk, etc...you can use it full range and be very happy. However, if you room is medium to large, and/or you listen at higher levels to a more diverse range of music, I don't feel that the PP-150 will be able to drive and control the woofers in an optimal fashion.
Chuck, I think it is going to be very hard to find a high powered tube integrated amp that really does the HT3's justice. Can you possibly go with just an amp? Can you provide a little more context around your room, listening preferences, associated gear, etc...? With a little more info, maybe we can come up with something.
George