1) Two places containing the API reference.

In your example documentation the API reference is included in one of
the chapters. Wouldn't it be better to just have it in one place - the
Haddock docs?  

The example is just a test of how you could create a full-customizable single document which includes the Haddock reference. Of course, the idea is that you could create documentation without any Haddock render directive (but keeping the cross references) and then, you could enable the attachment Haddock reference in the same document or in another document.
 
2) Integration with Haddock docs.

I think it would be best if the pages generated by this system and the
pages generated by Haddock would be integrated as much as possible -
both style wise (sharing CSS, structure, headers, footers, sidebars
etc) and also in terms of hyper linking. Identifiers in your
documentation should go to the Haddock docs. It should feel as if the
Haddock pages are just a part of the whole documentation structure.

I agree, and I tried to represent that in the example (but I created a new css). All the documentation will be rendered by Pandoc so there is no difference between the format of each side. I also think it would be interesting to be able to refer to parts of the documentation from Haddock, but keeping the Haddock format (This is not shown in the example).
 
3) Configuration

I haven't looked at this yet but I suspect people will not want
another configuration file in their projects. Perhaps you could
propose some kind of Cabal integration instead.

That would be awesome. I have to see how Cabal handles these files.