There's no one amp that is "best" for all headphones. Pete has even told me that the Pinnacle cannot drive the K1000 to ear-splitting levels (and some would extend that to the HE-6) though it can drive well. That still seems like another compromise to me considering the headphones you own, one I wouldn't be willing to make at 10K.
If I was in your shoes (and this is what I'll probably do) I'd keep the BA for the more efficient headphones (Grado through HD800) and get something like an LG for Audeze through K1000/HE-6.
I've only heard the LG twice but am getting one in for a longer time period fairly soon. That I plan on buying one to complement the BA says something about it taking up where the BA leaves off.
Edit- I still haven't heard one with more sensitive headphones, but have heard it may not be as an ideal pairing.
Edited by Radio_head - 1/2/13 at 3:48pm