People have suggested that on being summoned to the Headmaster's office, Harry precommits to time-turn back and hide Hermione's body before the summons arrives. Whether that means replacing the ring or the stone or what have you.

There are several ways I can think of that Dumbledore could circumvent this:

• keep Harry under observation for the next six hours, magically or otherwise
• force Harry to use all six turns immediately, and then keep him under observation for six hours
• check the Map (if he's the one who currently holds it; do we know at this point?) for multiple instances of Harry--a second Harry would be evidence that he'd been engaged in time-turner shenanigans

The first two methods seem wasteful. High cost compared to the relatively trivial transfiguration check. So if Dumbledore has other suspects besides Harry, he might not deem it worthwhile. The third is simple enough, if Dumbledore does have the Map. And if the Map does display multiple instances of time-turned people, as seems likely--I think this has been discussed as possibly being one of the "errors" the twins note.

Which still leaves the question of whether Dumbledore does have it.