Well, it can definitely be related to the type of valves you're using. Off the top of my head, it sounds to me like either a. the output of your preamp is clipping the input of the power amp. (You can try running the amp at full volume, and decreasing the output of the preamp), b. the input of the preamp is clipping, c. you are getting some kind of diode clipping (not sure if that's possible on the ADA, tho).
An easy experiment to try is swapping out the 12AX7s in your preamp with 12AT7s. These are much lower gain. You can then see if the tizziness is due to the preamp's input/gain stage, preamp's output, or power amp.