Well, it does pretty much put a hard stop on your appointment.  Hope you don't want to extend.

Enjoy.

of an hour or two without charge, if requested.

I've had that happen. Just call the desk and ask for a late check-out. In our case, the Provider said she was "sick" and needed another 30-45 minutes beyond her already 'late checkout' time cuz she was barfing (we were in perfect health).

Actually, I suggested that little gem so we were both laughing about it when it worked. It set a fun tone for our Sesh...

Since they have people checking in at all times of the day, they can stagger the checkout times the same way.

I have checked out of hotels as late as 4 PM for hotels which have a 10AM checkout.  They simply clean your room last...

Furthermore, unless they are absolutely full that night (a rarity under normal cases), they can let you check out late anyways, since they do not need that room anyways.

Do not worry about it.