I agree with everything you say about Charisse, although I saw her when understudy John Scherer was on for Schneider. She didn't even seem to be trying to find pitch when she did the songs, but she looked beautiful and she was touching. Montevecchi got some laughs in the role, probably a good thing, while Charisse got none, and Montevecchi sang it better (not saying much, and I do love "Liliane" howling in "Grim Hotel"), but Charisse really made more sense. Montevecchi did not convey vulnerability or fragility in the role, and that's essential.
Caron played it in Berlin.
Charisse did a stock tour of Illya Darling in 1968, and I would guess that she tried to sing a bit more when she did that.