A really cool update on this topic... @Rivkin it is interesting, and maybe even telling, that you initially thought the sword to be Hizen. As we know Tadayoshi's konuka-hada was an attempt at Awataguchi's nashiji-hada.
So the other day I was perusing Nakahara's Facts and Fundamentals book and came upon a paragraph in the Q&A section on page 53 that kind of changes the game in Awataguchi's favor for the original blade in question for this topic...as in Fukunaga might be correct with his sayagaki, unless anyone can show me an Enju blade that replicates what I am about to describe. Seeing as how I also have an Enju Kunisuke right beside it (and would consider him representative of the school) and the forging is nothing alike, it seems unlikely.
Hopefully the photos are not too low resolution to see, but when I first received and inspected the sword, I noticed what appeared to me to look like short, white dog hair in the ji-hada. I remember thinking that, because I have a white haired pit bull and saying to myself, this looks like her fur that sheds everywhere
So anyway, back to page 53...Nakahara says:
"It is written in sword appraisal books of around the late Muromachi period, the Rai, Awataguchi, and Ko-Bizen blades have masame-hada. This is rather difficult to interpret. I think that between that time and now, the difference in polishing techniques and the quality of the polishing stones used were somewhat different. What old kantei books referred to then as masame-hada was a condition of the hada that had the appearance of very short rabbit hair. This kind of description was also used for tea bowls. One type of Tenmoku (black glazed) tea bowl used in the tea ceremony is called Nogime-tenmoku (hare's fur Tenmoku). I suspect the same terminology was applied because of the similarity to the pattern of the tea bowl."
So after reading that, I was like wow ok so what does this tea bowl look like, because the short fur masame is definitely spot on.
See below for comparison