But just after Hermione's body dissappeared, they throroughly searched Harry's person and stuff for transfigured objects and finite incantatem-ed the lot.

The corpse could be transfigured into the necklace of the time-turner. This is such an incredibly stupid and dangerous idea that no-one would ever suspect Harry to do anything like this. Or he can transfigure Hermione into one chain link of the necklace (safer failure mode).

Are there any (known) size limits to the transfiguration? If not, there's plenty of room at the bottom...