Ah, Brett, I wish I had an "answer". I don't. I've had some ideas about genetic linkages of traits in koi floating around in my mind for some time, but I simply do not have the first hand knowledge/experience to begin to sort it out. ... It begins with Asagi and Shusui.
I think it too simplistic to refer to Shusui as doitsu versions of Asagi. The Hi on Shusui simply does not behave in the same way... different patterning and, as DickB has pointed out, a tendency in many for Hi to decrease over time, not expand as in Asagi. I assume the differences are tied to the doitsu carp bred into Asagi to create Shusui.
The "flank" patterning of Hi in Shusui and of Sumi in Kumonryu also appears to me to be derived from some ancestral carp, perhaps the original German carp? This patterning is more generally seen in doitsu fish. (But, sometimes it shows vaguely in Wagoi... a pond mutt Hariwake of mine has had Hi spread laterally on her flanks.)In Asagi the Hi will creep up from below, not too disimilar from the way Sumi will rise and spread from the abdomen in older Utsuri lines (not "tainted" by Sanke genes). The gold/orange bellies of some Karasugoi also seems to me to behave similarly to Asagi's orange bellies, at least on some specimens... I had one a few years back where you could see an orangish tone under/in the Sumi up to about the lateral line. (The belly had been silverish when only a few inches long, and became quite orange by 18", and seemed to spread upward under the Sumi until I got rid of the ugly thing at about 22".)
In Matsukawabake, the trait that stands out is the phenomenon of Sumi disappearing and reappearing. But, the Sumi patterning is often primarily from the belly to just above the lateral line ...much like the Aka patterning on Asagi.
You can probably think of other examples of Sumi on one type of koi behaving like the Hi/Aka on another type and vice versa.
It seems to me that there are genes dictating placement; genes dictating mode of expansion of pigment; and genes dictating doitsu vs wagoi; and genes determining the color of pigment. These have general linkages to one another that together "create" a variety; but sometimes the links become re-arranged. I think it interesting that you do not mention having doitsu Karasugoi in those old batches of fry, but do say all the Kumonryu had lateral flank patterning.... I think of that as defining Kumonryu. But, the Matsukawabake were in every sort of variation. So, was it a lethal combination for Sumi to spread from below on a doitsu fish, or is the link between lateral-flank patterning on doitsu scalation so strong that it is not easily broken? But with the wagoi, the genes determining placement and mode of expansion re-arranged randomly... genetic links were broken?? I'd expect Utsuri-type Sumi behavior in the wagoi to predominate, but not be exclusive.
Then there is difference in placement and behavior of Utsuri Sumi and Sanke Sumi.... which gets all mixed up in contemporary Showa with a large dose of Sanke genes.... I'm wanting a black and white koi with Sumi that is positioned and behaves like the Hi of Kohaku, with the lacquer of Sanke-Sumi. I can imagine the fish (and JR posted a pic once of a koi that came close). And, I can imagine a koi that is red and white with the Hi behaving like Utsuri-Sumi, with the pigment being the red of Kohaku... imagine brilliant red menware slicing across the face with Motobeni pectorals? LOL
Well, enough. I could ramble on a lot more, but I expect most everyone is bored by this and must think I'm more than a little nuts to think about this stuff with no practical application. If I ever make sense of it, I'll surprise myself.