Since you have been patiently adamant.
I'll keep my thoughts brief and let Pale Rider fill in in-depth context.
They compare quite well to the 009, with the caveat of being driven by a T2. I might admit even directly comparable out of a Carbon.
HEDD's Resolution and detail retrieval is a slight step down. However, what is quite rather remarkable is the HEDD's ability to extend without a hint of harshness. Only the T2/009 and SR1a have presented such an uncanny quality.
HEDD's mids are a little forward and quite detailed. The 009 matches this and exceeds in how smooth they are presented.
Both present well textured and extended bass, with the 009 feeling a tad bit punchier and the HEDD extending further down. Contrary to BS rhetoric of stats.
HEDD's stage is bigger, more enveloping and extended. Still the 009 is excellent if just a hair or two behind; it remains well separated and open.
009 has incisive imaging with great solidity -- more than I've heard any headphone save SR1a.
HEDD here is negligibly behind unless you are looking for it.
Closing: I think the HEDD would make a wonderful complementary addition if you wanted to stay within the same sound signature.
I might add consideration for the SR1a as well.
If you wanted the slightly different signature as alluded, perhaps the Abyss with it's own can of worms.
IMO of course.