Some thoughts on "Hermiones brain will be transfigured and kept frozen by Harry":

We know from Harrys first transfiguration lesson that transfigured living things undergo changes with time, which will kill said things. Harry knows this, and is thus likely to thing of deep-freezing the Hermione-diamond. Only he also plans to retransfigurate his fathers rock, and we know that one sustained transfiguration is a serious drain on his magic. Add to that the magical drain from having to cool the H-diamond and its thermal buffer, I think it unlikely that he did something of that sorts.

One way to circumvent the drain of the transfigured H-diamond would be to make it microscopically small, but he still would have to touch it regularly; given that its temperature should be in the cryogenic range, only touches with his wand would be feasible.

The only way I can think of to circumvent these problems would be to have others partake in the task, but that brings with it other problems.

Any thoughts which theories Harry tested with

"Is that a usual tactic, by the way?" Harry said, voice still odd. "Carrying something large Transfigured into something small to use as a weapon? Or is that a usual exercise for Transfiguration practice?"