I'm not sure about the 17-40 being magical or not on APS-H, but I was quite happy using it on a 1d3. The 17-40 is quite weak in the outer portions of the frame at the wide end, but on APS-H those portions are mostly cut off.
The sigma 12-24 is not that strong of a performer, but it is certainly the widest option with >APS-C coverage.
The Tokina is an APS-C lens, but if I remember right it covers the APS-H image circle from about 13mm and up. If you are ok with the limited range, it is a very high performing lens. Some people complain about flare, but I found that shading the lens with my hand was usually sufficient to prevent flare in all but the worst situations.
So my choice would be 17-40 if you don't need ultrawide, Tokina if you specifically want ultrawide, and the Sigma if you want ultrawide plus the extra zoom range on both ends over the tokina (at a performance cost vs. the other two lenses)