He had more experience than I, he having produced more than 10 songs already.
He had more experience than I, him having produced more than 10 songs already.
The latter sounds more natural to me, but the former seems more grammatically consistent—alas I don't know what the parts are called to delve further. The questions Is "all that he have" correct? and https://english.stackexchange.com/questions/119167/he-have-a-point-is-this-correct were all I could find and didn't seem specifically relevant, AFAICT.