A lot of the trouble in interview processes is communication or an overflow of work that causes seemingly "closed" interviews to fall off people's priority list

A lot of the trouble in interview processes is communication or an overflow of work that causes seemingly "closed" interviews to fall off people's priority lists. For you, specifically, I'd recommend preferring the future regret of having contacted the head of hr later than is advisable than the regret of never knowing. After all, the worst thing that could happen is they say no, whereas all slightly less bad consequences are pretty rad.