That great one from ASSASSINS....Samuel Byck's one.
"You can't overrate Bernadette Peters. She is such a genius. There's a moment in "Too Many Mornings" and Bernadette doing 'I wore green the last time' - It's a voice that is just already given up - it is so sorrowful. Tragic. You can see from that moment the show is going to be headed into such dark territory and it hinges on this tiny throwaway moment of the voice." - Ben Brantley (2022)
"Bernadette's whole, stunning performance [as Rose in Gypsy] galvanized the actors capable of letting loose with her. Bernadette's Rose did take its rightful place, but too late, and unseen by too many who should have seen it" Arthur Laurents (2009)
"Sondheim's own favorite star performances? [Bernadette] Peters in ''Sunday in the Park,'' Lansbury in ''Sweeney Todd'' and ''obviously, Ethel was thrilling in 'Gypsy.'' Nytimes, 2000
There is a monologue from Sunday in the Park with George that, although in the published libretto, is cut from the production. It's right after "It's Hot Up Here".
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."
The comment re monologues in musicals are songs is most apt.
That said, BOBBY's monologue about the date with the girl in the motel is a fun one. It's right after April's "Butterfly" monologue....though quite short. And if memory serves, doesn't "Arthur" have a monologue (of sorts) at the end of Act One in CAMELOT?
THAT said, you might look over some songs which are more word-centric than melody-centric, and see if you can make it work without the singing. Some classic plays are in verse, so it's possible to disconnect the music and have something you can act without the tune. "Adam"s song "EVE" in "The Apple Tree" works well this way, actually. (If nothing else, it's an EXCELLENT exercise in interpretation, and I've used it many times as an actor.)
I think we forgot one of the best known. Cornelius's from HELLO DOLLY, which is perhaps word for word the same as his famous monologue from The Matchmaker. O very close to it.
Ted and Phil have some hilarious and some heartbreaking monologues in "Three Guys Naked From the Waist Down", the great, short-lived off-Broadway musical that gave us Scott Bakula.