Although it takes some work, it is possible to hand-edit .csproj files in order to set up conditional referencing by adding a Condition
attribute to the appropriate references.
EDIT I've moved these conditions into ItemGroups, as it seems this is how my mentioned production code is working, and there has been mention of this being a possible issue in VS 2013.
<ItemGroup Condition="'$(Configuration)' == 'Debug Local'">
<!-- Library A reference as generated by VS for an in-solution reference, children unmodified -->
<ProjectReference>...
</ItemGroup>
<ItemGroup Condition="'$(Configuration)' == 'Debug NuGet'">
<!-- Library A reference as generated by NuGet, child nodes unmodified -->
<Reference Include="LibraryA">...
</ItemGroup>
This would allow you to have, on the Projects D & E, configurations of "Debug NuGet" vs. "Debug Local" which reference the libraries differently. If you then have multiple solution files which have their configurations mapped to the appropriate configurations on the projects within, the end user would never see more than "Debug" and "Release" for most operation, since those are the solution configs, and would only need to open the full solution for editing the A, B, & C projects.
Now, as for getting the A, B, & C projects out of the way, you could set them up under a folder marked as a subrepo (assuming you're using an SCM that supports this, such as Git). Most users would never need to pull the subrepo since they're not accessing the ABC projects, and are instead grabbing from NuGet.
Maintenance wise, I can guarantee that VS will not edit the conditional references, and will respect them during compilation -I have gone through both VS 2010 and 2013 (EDIT: Professional version, though I have delved into doing the same with express) with the same conditional reference projects at work. Keep in mind than in VS, references can be made version-agnostic, making NuGet the only place from which version need be maintained, and that can be done like any other NuGet package. While I'm hopeful, I have NOT tested whether NuGet will fight with the conditional references.
EDIT It may also be prudent to note that conditional references can cause warnings about missing DLLs, but does not actually hinder compilation or run.
EDIT For those still reading this, I'm now (7/2019) hearing that the IDE isn't as friendly to these changes anymore, and either it or the Package Manager may override them. Proceed with caution, and always read your commits!