They might frown on that, but that is how I would have written it.
It is like a t-shirt I saw recently:
"Let's eat, Grandma"
"Let's eat Grandma"
COMMAS SAVE LIVES!
Eh. I think the parenthesis probably makes it sound like an aside, when it is key to the story.
There are five commas, which seem a bit much to me (though I routinely use a lot as well, but...I don’t write for a living) which chops it up a bit.