Seems like to get it to work at such a sharp angle, you would need a very large depth of field with your lense in order to keep both the nearest and farthest portions of the page in focus.
I do have a phd in a theoretical quantum optics, so no, I have no idea if such a weird angle will actually work in practice given the physical and budgetary constraints. :-D
Seriously, though, I have idea. We can take two pictures focusing once the near part, and once on the far part.
If cameras are cheap (I haven't researched), maybe two on either end of the device would mitigate the complexity of the lenses required.
Depth of field isn't really an issue with wide angle lenses for smaller format sensors. The EFL is shorter which boosts the depth of field. The bigger problem is field curvature if the page is closer than ~6" - most of these lenses weren't designed for short object distances.
