Seems like that would only help if the duration of the blast was less than 24 hours

Or perhaps more like 12 hours, as half of the Earth would be exposed instantly.

But even then it depends on whether it's the direct radiation that's the issue or something more indirect (atmospheric changes, etc.)

doesn't this depend on the blast's origin relative to the Earth's axis?

The longest gamma ray bursts only last a few minutes.

Just how many nines reduction from peak intensity after a few minutes are we talking? Because I'd imagine 0.01% of a nearby gamma ray burst would still be bad news.

Rotation around the axis doesn't expose the northern hemisphere to the southern sky, nor vice versa.

That depends on the orientation with regard to the poles. If the source were directly over a pole, only fifty percent of the planet would be directly exposed. If it were over the equator, however, the whole planet would be, if it were a magic GRB that lasted way longer than usual.

So the upside is that anything that can get through 10k km of rock is very unlikely to interact with anything on the other side (eg neutrinos)

It will affect atmospheric chemistry. It will produce a ton of NO2 and make atmosphere unbreathable without equipment.

I imagine that killing half the planet is enough to send the "lucky" half into chaos and collapse.