I know an older gentleman who used to own Consequence. He has gone thru many amps, from high power solid state like Bryston 7B-ST to a 70wpc tube amp. His favorite was the medium power tube amp that was made in Canada, but the company has gone belly up and I can't remember the name at this moment.
I used to own Confidence 5 which many believed are the modern iteration of Consequence. I have tried 10+ amps on those and I would not recommend tube with them. The best tube amp I had success with was Sonic Frontiers Power 3, but even then they could not fully bring out the bass.
If you are not dead set on Consequence, I suggest you look for a new speaker that has more resolving power, quicker, more transparent, and easier to drive. As much as I loved the Confidence 5, I have moved on and much happier now.