I have a friend who also stutters, or, I found out he stutters after knowing him for a few months.
Apparently he uses a similar technique where he "sings" what he wants to say in a slightly higher-pitched voice when talking in a professional setting. He sounds totally normal when using it, but you're not in doubt when he doesn't.
The speech and singing regions of the brain are separate from each other, which is why this works. It also can work for people who lose the ability to speak from brain damage.
It's wild how adaptable the brain is. Some dude was out there just living life when he had a head mri after a car crash (iirc) and found that he only had a brain stem.
To quote ancient words of wisdom: "Everybody's sayin' that the Scatman stutters but doesn't ever stutter when he sings. But what you don't know, I'm gonna tell you right now that the stutter and the scat is the same thing, yo, I'm the Scatman."
Voice resonance has more to do with your body/skull structure than anything. One thing that I find interesting is that most phenomenonal singers have rather large mouths. My singing ability actually improved as a child after getting my jaw expanded.
You can kinda test this out yourself. Hold a note with your arms by your side, then again with your hands on top of your head with elbows out. Your voice will have a lot more resonance because you're expanding your chest (this is also the best position to catch your breath in)
Source: classically trained musician taught by PhDs in the various instruments I can play (including singing)
I also have a fun breathing exercise that will make you super light headed, which is fun.
On a related note (heh) walking and dancing are also controlled by different brain areas. One of my neighbours has episodes of neurologic muscle spasms that can make her unable to even stand... So when it happens she starts shimmying sideways, or doing little hops. She's absolutely adorable.
I actually had my own bard character based on this premise, Ré Mí the Eloquence Bard, a Kenku who learned to sing speak to overcome the Kenku speech impediment.