If you can find a Dynaco ST35, its a lot more linear amp than its bigger brother. But it makes about 17 Watts/channel.
SETs tend to have a limited amount of what I call 'usable power'. By that I mean its usually not a good idea to push them past 20-25% of full power. Based on your comments your speakers are nowhere near efficient enough to work with your SET.
If that 96dB number is real, your speakers are similar to mine which are 98dB. I find that I need a bit of power; at least 30 Watts. I have an average room, so I suspect you'll need at least that much.
So the amps you are looking for (if you stay with tubes) will be PushPull. They tend to have a much higher amount of 'usable power'; usually close to 95%.
The ST70 is not a bad suggestion in this range; the RM10 is another good one. Either should be properly refurbished. Another amp that might suit is the Harmon Kardon Citation 2 if you can find one refurbished. They make about 60 Watt/ch.