I like your definition of Mmmm and Aaahhhh better.
Changing pitch on the leadpipe is a bitch; it’s easier on the mp or horn.
If you focus with your eyes closed and lips on the mp in your horn as you “say” (think) Ohhhhhhh, you should feel the muscles in your face at the sides of the aperture; engage those muscles as you ascend my arching your tongue as usual (aahhhh eeeee) and tightening the corners by tightening those muscles.
That’s what worked for me and was my initial”coffee moment” FWIW.