It would be the same as draw. 1/2 - 1/2
Why no notation for stalemte?

It would be the same as draw. 1/2 - 1/2
A draw isn't necessarily a stalemate. It can be from perpetual check, "positional draw", three-fold repitition, or draw by agreement.

It is bugs me like hell there is no notation for stalemate. Jus sayin'
8th line in your list, is the correct annotation

"1/2-1/2 draw by stalemate" looks good to me. I wish the newspapers and books tell us how they win whether is by resignation or time.

Maybe S for Stalemate? Or possibly halmos tombstone.
I'd use the vertical lines from the checkmate. Similar to this "//". Seems to correspond with the checkmate symbol.
This oughta be a candidate for "Stuff non chess players say" hehe
Btw, I like the twitter symbol or the fence symbol for checkmate. Wonder how it got started.

Why not for 3-fold or 50 moves or draw by agreement?
This makes more sense because it may not be immediately obvious when playing over the score.
Also a symbol for loss on time.
It seems the only reason you want a symbol for stalemate is because it happens to have the word "mate" in it.
I think it should just be "=". "=" is an evaluative term, so does it ever actually show up in the move list? Perhaps if the player is writing notes to himself during an otb game? Otherwise it could denote all forms of legally forced draw, like repetition, 50 moves, or stalemate. I assume draw by agreement would be the exception, since it's a draw that isn't inherent in the position, so to speak.
It is bugs me like hell there is no notation for stalemate. Jus sayin'