Harry has already upgraded two existing spells: partial transfiguration and Patronus 2.0

In both cases, he achieved the impossible by ignoring what wizards believe and instead concentrating on his own beliefs.

What does Harry believe about Hermione that other wizards do not? He believes she is a purely biological machine, that there are no souls, and that a reductionist viewpoint is correct.

Therefore, in the right frame of mind, perhaps Harry can reparo a dead human (although canon!reparo cannot repair magical items properly, I wonder if it might restore Hermione without her magic, and if she might just be just as awesome without it.)

The biggest problem I see with this is that in the past, Harry felt his father did not take him seriously. However, he now has power his father knows not, and he has resolved to do anything to bring her back - he could credibly threaten his father's career, for example.

If his father does not take him seriously, then credible threats are both difficult and costly (because once you have made the threat and they dismiss you, then you need to follow through).

Harry is also bad at threatening, and so I would not recommend it to him even if it were optimal for one with more skill.

Multiple FF.net reviews suggest getting Harry's parents to try and cheer him up. But what about this, before the beginning of chapter 1:

Petunia married a biochemist

I predict Harry might realise his father can help him and find a way to ask/make him help. All the PCs and powerful NPCs around him want Hermione to be dead (either through action or inaction). If she can be revived, a professor of biochemistry might just have relevant knowledge, equipment, and the will to act. Come to think of it, even more so might Hermione's parents.

The biggest problem I see with this is that in the past, Harry felt his father did not take him seriously. However, he now has power his father knows not, and he has resolved to do anything to bring her back - he could credibly threaten his father's career, for example.

The second problem is that Harry may be too wrapped up with being responsible and needing to fix this himself to think of asking anyone else for help, but signalling him via Patronus is at least worth a try and costs little - "We are in a war situation, my best friend was just killed by a double traumatic leg amputation, but I've cooled her to 5 degrees and trying to work out what to do next. Ideas? I am deadly serious."