We used to be pretty heavily into blotched kings back in the late '80s and early '90s, when they were still pretty rare. We spent quite a bit of time discussing them with some of the first people who collected them, bred them, and researched them, mainly Art Meyers and Bruce Means. After a lot of discussion, it is my opinion that the "true" goini was a striped / patternless king that was separated from the other populations, such as the eastern king, by geographical features a long time ago. But when the geography changed, it interbred and became diluted. So I believe that now only a relict population occurs in the panhandle of Florida, and has been pretty well intermingled with other kings from the surrounding area. I believe that is why you will only occasionally find a striped or patternless animal. In my opinion, the blotched king that is usually shown in photos in books is really an intergrade, and is not the "true" goini, which should be the striped or patternless snake, with a speckle on each scale.
Interestingly, the striped / patternless appearance seems to be at least partially sex linked. Almost all of the wild caught animals with that pattern (or lack of pattern) have been male. And if the patternless wild caught is bred to a typical blotched, almost all of the stripey babies will be males. However, if you breed the most atypical, stripiest individuals (esp. the few females) together for a few generations, you can start to weed out the blotched patterned snakes and start to get more babies (including females) that are striped / patternless. It was a fun project for several generations. But once we started producing plenty of the non-blotched babies of both sexes, the project lost a lot of the excitement to see what could be done.
Of course, all of my info is many years old, since I have not been folowing what is going on with them since I stopped keeping kings many years ago. And of course, I am not a taxonomist, so the above is just my own opinion of what they are / were.