Thank you, I am considering the gain reduction mod but in the meantime I added -10dB Rothwell XLR attenuators between the BDA-2 DAC and BHA-1. And it is working pretty well.
The BHA-1 excessive gain became even more apparent when I replaced the pair of 2B LP PROs with 4B SSTC. Even with BHA1 on Low gain and 4B SSTC sensitivity set to 2V, that what I assume should be for balanced connections, I could not move the BHA-1 volume knob past 9:3- or 10. After a couple of hours of listening the attenuators do not seem to have any bad effects on SQ, the bass seems actually more pronounced and better controlled, which is probably because now I can actually use the BHA-1 excellent volume control to find a sweet spot for listening to different tracks.