Just thought I'd add my own two cents FWIW.
I own both the LLmk1 and LLmk2, so I'm in a unique position to hear them side-by-side. There is a definite improvement in the mk2 to my ears. In fact it's honestly a bit surprising to me to hear just how much of an improvement results from changes like working on stray capacitance, but it's there. The LLmk2 is more nuanced, and subtle details and layering are much more apparent. I find the LLmk1 to be more restrained or polite by comparison, laid back. The LLmk2 on the other hand literally throws details at me, yet---at this is the crucial part for me---it remains effortless and musically engaging.
While I've always appreciated the truly exceptional driver control of both the KGSS and BHSE (I have not yet heard the KGSSHV), I've always personally preferred the LL in terms of its overall sound. It just sounds more natural or "correct" to me. When I got my LLmk1, I eventually said goodbye to my KGSS as a result. I went ahead and ordered a BHSE however because I still feel it pairs quite well with the SR-007 which truly benefits from its tight grip. When it came to the SR-Omega and SR-009 however I preferred my LLmk1 to the BHSE in terms of tonal synergy. Now with the LLmk2, I honestly feel my BHSE order is redundant, as the LLmk2 can in my humble opinion easily keep pace with the BHSE in terms of performance. I'm sure some folks will think "yeah right" when they read that, but there you go. I personally feel the LLmk2 is the best commercial stat amp I've heard so far with both the SR-009 and SR-007 (and SR-Omega).
Yes, I also prefer it to the Electra.
I still keep the LLmk1 btw to use in my office. It essentially replaced my SRM-717's duties, as I find it an improvement over the Stax amps. I still have my BHSE on order, as I really do like Justin's build quality, and I'll probably use it for normal bias Sigmas and as a backup amp for the SR-007s. Hopefully I'll get to hear the KGSSHV some day soon, but from impressions by those who I can calibrate my own taste to, I suspect it's not for me.