It's an interesting analysis, but it feels like there really isn't much difference between NY and SBY (except for one I'll address below). That is, the only difference I can see is that, in SBY, the players have a more overt responsibility to be as proactive as possible, while NY they should still be proactive, but not being all-proactive all the time is fine. In pretty much every other sense, though, your analysis seems to put the two very close to one another. Basically, their only difference is the degree to which the players need to be "taking the lead" in terms of what matters and where the action "goes".
Conversely, RRY seems to be distinctly different from both of the other two at almost every turn, except that very last one...which I'm not entirely sold on?
That is, there is no need to "reframe" anything at all in the RRY approach. The GM just declares what they wish to declare; the players are simply along for the ride regardless of what the rolls say. In NY, it's necessary, and in SBY, it's simply a greater challenge because, as before, the players are required to furnish more than a minimum amount of information. They need to be pretty proactive, as before; it is possible for the GM to struggle if the players simply aren't giving them enough to work with, but far from guaranteed. Hence, it's not that the technique doesn't work, it's that the technique doesn't work for a GM acting autonomously.
And I think that's a pretty big kicker here. In both NY and SBY, the GM cannot act entirely autonomously. The only meaningful difference between NY and SBY is that sometimes the GM can act autonomously in NY, but she is nearly incapable of acting autonomously in the most extreme versions of SBY. In RRY, the GM not only can act entirely autonomously, they always act autonomously.
That's a pretty big difference, and shows how NY is much closer to SBY than to RRY. In NY, it might be the case that the GM can act autonomously, but it's not guaranteed to be possible--some of the time, they won't be able to. In SBY, it's rare to nonexistent that the GM can act autonomously--so both have a presumption, unless proven otherwise, that autonomous GM action is not guaranteed. RRY has autonomous GM action not only guaranteed, but outright enforced, all the time.
Can we come up with two additional methods that would fit into the missing spots? That is, it seems to me this reveals a pretty major gap: there should be a #Y where autonomous GM action is always possible but never required (the exact midpoint between SBY and RRY), and a separate $Y where the natural state is the GM acting autonomously but it isn't guaranteed that they will.
Or, in more tabular form:
RRY : GM functionally always acts autonomously, barring extremely rare exceptions
$Y : GM is presumed to act autonomously, but might decline to at times
#Y : GM always can act autonomously, but never has to; no presumed bias either way
NY: GM might be able to act autonomously, but is never guaranteed to be able to
SBY: GM functionally can't act autonomously, barring extremely rare exceptions
For me, I find that the vast majority of D&D games that bill themselves as "sandbox" games are closer to NY, or (occasionally) #Y, whever we choose to call it. Games like pure no-myth PbtA or Ironsworn are full-throated SBY, especially the latter, since it doesn't actually need to have a GM at all. Further, most games that are railroad-y are $Y, not RRY; it's actually pretty rare to get something as utterly extreme as RRY (hence my use of "Dragonlance-style" etc. as my term for this sort of thing, as that's one of the rare places where D&D goes so far as to assign individual characters and even spoken lines to specific players.)