Let me qualify my remarks by saying I know just enough about economics to make me dangerous [though one of the transfer pricing economists I work says that is an apt description for all economists also :) ].
I noticed you used a neo-classical growth model and exogenous growth functions as the basis for your analysis. Might endogenous growth theory be a better fit for the AI scenario? Or at least wouldn't it be interesting to see what predictions an endogenous model might make? From what I remember of endogenous growth theory, the way it models growth seems to match better an economy where AI was advanced.
Another area that might warrant further review is the neo-classical idea of diminishing returns. I know Paul Romer alleged that the diminishing returns problem might not apply if capital was expanded to include human capital. However, an interesting analysis (which I'm not capable of performing :) ) is what would happen to diminishing returns where capital became based largely on knowledge, heuristics, and other AI areas. Coupled with the idea of positive feedback from technological change (and AI development, e.g. Vinge's singularity), it looks like a strong case could be made to throw diminishing returns out the window (or at least put it in the closet and see what the models do then).
One last point is the idea of efficiency. I read a paper a year or so ago in the Journal of Economic Perspectives (I'll try and locate it but can't at the moment) that stated some poor countries would do well not to worry about acquiring more of the right resources but instead work towards wasting less of their existing resources. What impact might a drastically increased efficiency in capital utilization have on growth models? How would this potential effect of AI-development be factored in to growth models?