Wasn't there a story about someone who accidentally Polyjuiced herself into a cat and, instead of getting help, hid from the teachers, so she got stuck cat-like? McGonagall could turn into a cat and Polyjuice herself into Hermione from that state, to get the effect deliberately. The waxy, doll-like appearance could be a side-effect of deliberately botched Polyjuice. Or... Hermione could Transfigure McGonagall. Hard, but quite possibly just within her capabilities, with guidance.

The ward message is a problem, but, as jaibot suggested, maybe McGonagall enrolled herself as a student. Or maybe the wards sound the same for students and teachers, and Dumbledore interpreted it when he saw "Hermione" dead.

The description of the death scene is Harry's interpretation, not objective truth.

At this point in the narrative, I can add epicycles to deal with the problems, which is just as it should be. It is a beautiful theory (and my baby!), and I still have a few hours before the really ugly facts show up.

Edit: And here they are. The tragedy of theories strikes again…

I think Harry spent the time sitting in front of the room planning what he was going to do to revive Hermione, because what went wrong when he got her killed was largely due to time constraints. It is explicitly stated that he was there for hours, and Minerva says it looks like years have passed when he comes out. So, I also think that whatever Harry planned, and then tried for several hours, did not work, and he came out with Hermione still dead. He is saying that there is nothing left to plan at the beginning of 92, whereas after he cools Hermione he thinks that he now has time to think. That strongly suggests he thought, tried the plan, and it failed.

On the other hand, Minerva has been told explicitly that people have generally not done everything they can, teaches Transfiguration, and quite definitely feels terrible over Hermione's death. She is also free to use the Time-Turner. So, yes, I also think she went back, Transfigured herself into Hermione, and let herself be killed, as that was, by that point, the only way to save Hermione's life. She probably borrowed Harry's invisibility cloak to hide Hermione from all the people who mustn't know that she is still alive if she is to survive. That hasn't happened yet, but there is still time. (Note that she also identifies with the other specified victim of the troll, Mrs Norris.)

This is well within Minerva's capabilities as stated, explains who was asking for the troll to be led away (Hermione under a cloak), and fits with Dumbledore's comment about losing another friend instead. It also has the potential to appease the feminists, because Hermione is saved by a woman acting heroically after Harry has failed.

I also find it a lot easier to live with. My reaction to death has got stronger as I've got older, and I cope a lot more easily with someone sacrificing themselves to save someone else than with someone just being killed. Agency matters. I still feel a bit sorry for the troll, though.