You aren't "gaming the system." You are keeping your room until check-out time. Telling the desk "I need the room until noon even though I'll be removing my luggage earlier, and it may appear vacant" should be fine.

I recently almost did the same thing, as I had booked a "24 hour" room period @ LAX (Four Points) and needed it only for 8 hours initially, but given the chance of cancellation/serious delay, almost didn't check out, thinking I may need to come back and use the room to spend the night - I figured I'd just call the hotel when I was about to board the plane that night.