@Ephraim0Well, God bless you for being so kind and accomodating. Unfortunately, check-out time is sacrosant, it should never be left up to chance, meaning up to the guest to 'get it', nor interpret it or ignore it, otherwise you now see what could (and did) happen.
If it was me, I would make it 11am btw, which is a somewhat standard time for check outs. And at exactly 11am, the 'cleaning crew' shows up and starts making its presence. :).
As to the private feedback, it is cool to educate the guest, helps everyone in the long run, though I would make it more informal: 'Thanks for staying with us, but please remember check-out times are important for hosting places, very important. Wish you pleasant journeys and till next time...".
In other words, *I* would take responsibility for the whole fiasco.