[Retros] Fastest selfmates in 1?

[Elkies, Noam]

This question is mainly for Francois Labelle, but possibly
others here may be interested, and/or aware of relevant work.

How quickly can a legal game reach a position where one side
must give checkmate, and what are all such minimal-length positions?

I do not ask for the position to have a unique helpgame / proof game;
naturally that's of interest too, but the shortest such game is probably
still beyond the range of exhaustive computer search.

The question was suggested by a now-deleted answer on
Chess Stack Exchange that may still be visible at the URL
https://chess.stackexchange.com/questions/33154/what-is-the-fastest-way-to-reach-a-position-in-which-one-side-is-forced-to-choos/33162#33162
, which gave a 6.0 move game (White is forced to mate on move 7).

I found a 5.5 move position, and posed it as a puzzle
<https://chess.stackexchange.com/questions/33168/>.
That position wasn't found yet, but Rewan Demontay remembered
that Tim Krabbe wrote about this puzzle in entry #153 of his
Chss Diary (<https://timkr.home.xs4all.nl/chess2/diary_8.htm>,
"Gamehelpselfmate") which gave two other 5.5 movers by
Pim Blijlevens, and then a third by Sasho Kalajdzievski
which would even work with Black passing one ply.
(Krabbe counts these as 5.0 moves to a S#1 position.)
None of these is what I found, which -- as I wrote on Chess
Stack Exchange -- is two very similar positions with a total of
660 possible 5.5-move games [Popeye 3.41].

It should be possible to extract the answer to this question from
Labelle's exhaustive databases in several ways, e.g. the lists of
positions in at most 5.5 moves with one side in check.

Thanks,
--NDE

P.S. While I'm at it, is there a faster game than my 12.0 moves
for R. Demontay's actual question 33154 (to reach a position where
the side to play must choose between giving checkmate or stalemate)?