The BHSE doesn't bring the 007 to 009 level. The 009 definitely still is superior on detail extraction since the 007 naturally has a dark signature. To get a similar level of detail on the 007 on the BHSE, I have to turn the volume up beyond the levels I normally listen at.
That said, the BHSE accentuates characteristics of the 007 I personally find very enjoyable, without compromising the non-fatiguing character of the 007. The 007 is still the most non-fatiguing headphone I've ever heard, and if I'm going to be listening to music for several hours on a headphone, I'd reach for the 007 in a heartbeat. The BHSE does really nice things with naturally expanding the soundstage without making the headphone sound overly resonant and gives the bass a satisfying level of presence. It's not HE6 or LCD3 impact, but the bass on the BHSE+007 seems to have more discernible texture than a well-amped high-end ortho, though it's not nearly as speaker-like as the HE6 is. The proto LL actually made the 009 more 007-like to my ears which is why I thought the proto LL+009 pairing was nice. Even on the BHSE, the 009 has etch to my ears, but I'm very sensitive to brightness and etch. I'd need to listen to the LL again to decide more conclusively if it had a similar level of etch, but I do remember the LL mellowing out the 009 qualities I don't really care for. A lot of it will come down to what your preference for musicality is.
Build quality on the BHSE is sublime. I don't think you can do better in headphoneland. It'll take a significant change in personal circumstances for me to part with the amp.