"Daddy, can I go to ... uh Excuse me, Dad, Would it be OK if I ... Dad, is it acceptable if I go ... Dad, Excuse me, but after I get all my chores done, do you think it would be acceptable if I went ... "
That's what my 7 year old does when he really wants to say or do something that's important to him. He gets too caught up in the 'proper' way of asking to get the question across. He doesn't really stutter, but he takes several false starts to get the info out.
My daughter does a stutter stumble at the end of words as if she is replacing "Uh" or "mmm" or some other place holder by repeating the last phonetic combination. It sounds similar to what you have described.
It mainly happens on days that are already shot for one reason or another.
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It's just music for me. The other stims don't work.