I wanted to poke my head in here and mention that I'm one of those nuts that runs his headphones directly off the power amp speaker taps.
I've never had the pleasure of hearing a BHA-1, but I currently have a 2B and run my speakers off the binding posts. Actually, I know there's a headphone jack in front but it has resistors in-line... so I took those out

Interestingly, I prefer the sound of the 2B over the 3B and 4B with my Hifiman HE-6. However, the 3B and 4B that I have are quite old (pre SST era). One of these days I'd like to hear an updated model.
I just recently acquired a Stax SR-007 as well, and have been connecting those to the Brystons through a Woo Audio WEE transformer box. I modded one of the ports to bypass the transformers, but unfortunately even the 4B doesn't have enough gain to drive the 007 directly.