Looking at your movie again, I notice that every time we logged "We think topmenu style is NORMAL but it is actually FANCY", you had either:
1) Just visited the Account page - and changed to mobile mode, or whatever - and then did something which prompted KoL to refresh the awesomemenu.
2) Just visited awesomemenu.php?icons=1
I submitted a fix which did not "correct" menu style to "fancy" in case 2.
And now it is only case 1 which is screwing up.
So, yes: it was the Account page not recognizing the "fancy" radio button and setting TopMenuStyle to "normal" that was the root cause.
That fix is now in r27506.
(That still includes not even trying to decorate awesomemenu.php?icons=1)
If you are unable to reproduce any more "We think topmenu style is ..." errors, I will make a final (?) submit to remove the debugging code that does text searches in TopMenuDecorator to figure out what style you have and simply trusts that the style is correctly set by MoonPhaseRequest and AccountRequest, as appropriate. The awesomemenu.php?icons=1 fix will remain, since it need not (and can not) insert a script dropdown in the JSON.