There's a yet-simpler possibility.

Slowly the boy sat up in bed, his hands momentarily fiddling beneath the covers.

He's not stupid, he knew that he would be summoned when her body disappeared, so he slept with whatever her body is transfigured next to his skin so that it wouldn't reverse itself and then removed it in that first moment. No Time-Turner use required.

Now show me your pouch."

"It's in my trunk -" Harry began.

"Severus," said the old wizard, and the Potions Master moved forward. "Check his trunk as well, every compartment."

I notice that there are no instructions to check anywhere else--such as under the covers on his bed.