As Rick lead to in his comments to his original post, you can indeed extend the DXA implementation along with a custom TBB that gets your required data into the Navigation JSON. I've done similar with component links in SG metadata. This is a good post to start on your TBB: http://www.tridiondeveloper.com/quick-tbb-serialize-component-as-json
There are also some handy methods/helpers provided in the base classes that I began to uncover that you may want to explore in the open source first. Admittedly in our implementation there currently exists some quirks regarding the default mappings in the dxa application vs how the data is being deserialized into our custom models (be careful for any embedded links containing internal or external fields).
I did find it odd that all of the Navigation bits (GetNavigationModel) are being built off of the GenerateSitemap.cs and SitemapItem model. If approached correctly with that in mind however, it will work just as well as pre DXA navigation implementations.