Thoughts on SS bass. Tube mid and high tube pre

What is the input impedance of the Heil speaker by itself?  I bet it's on the low side, but I don't know.

If you’re running a sub you likely already have SS bass. Try without the Heil. I bet the overall bass improves because you’re doing your main amplifier a big favor by increasing the impedance it has to drive. Just try it.

Based on what Dover suggests, if you were to bi-amp, why not run a separate amplifier to the Heil tweeter? While that would do nothing for power demands in the bass, it would at least reduce the effect on impedance of running the supertweeter in parallel with the Tannoy. (The two speakers in parallel reduce the net impedance seen by the amp, as I am sure you know.) The resulting increase in the impedance seen by the tube amplifier can only help it to cope with power demands. (Tubes do better as regards both power output and distortion when interfaced with higher impedance speakers as compared to the net of 4 ohms you may be dealing with now.) Also, or as an alternative, add a subwoofer with its own amplification.