I had the AHB2 speaker amp, not the HPA4 headphone amp. Unfortunately I sold it before getting the TC, but I have a feeling that the TC would sound great with it (the AHB2), and that it might synergize even better than with the Susvara, for instance.
Reason being is that I felt the AHB2 had a kind of "dynamic ceiling" in general (and not just with the Susvara). But because the TC is so naturally strong when it comes to dynamics, this might not be as much of an issue, thus letting the strengths of the AHB2 to come out with less of its limitations dragging it down (ie, sounding a lil "polite").
This is just speculation, though. Also, I can't say if driving the TC or other planars off the headphone amp version versus the AHB2 speaker amp would result in the same listening experience. Subtle differences in the resulting sonic signature between the two could easily tip the scales in one direction or another. People tend to assume (ie, speculate) that they'd sound essentially the same, but I'd have to hear them side-by-side to be properly convinced.
On the question of resulting tonality (and also, relatedly, of "tonal density") of the TC with one of the two Benchmark amps, that to me is an even more complicated question to reason about without hearing them in person. Aaand now I'm curious again...