Experimental change.  Added a build of the reference assembly using PCL profile 259.  Notes below.

In Visual Studio 2013, if I bring up (a copy of) the profile78 project, I see target
platforms including ".NET Framework 4.5" and "Windows 8" and "Windows Phone Silverlight 8".

(Did the name of wp8 change from "Windows Phone 8" to "Windows Phone Silverlight 8"?)

Profile 78 is also supposed to include Xamarin iOS/Android, but Visual Studio,
somewhat unsurprisingly, doesn't know that.

If I change the targets to add "Windows Phone 8.1" by checking its checkbox,
the profile in the .csproj changes to profile 259.

So for now, I'm adding a build of the reference assembly for profile 259.

I'm expecting the Xamarin tools will dislike this.

According to the following page:

  http://embed.plnkr.co/03ck2dCtnJogBKHJ9EjY/preview

  profile 259 does not support Xamarin.

As of this commit, the solution still builds under VS 2012 with no problems.
That's interesting too, since profile 259 includes a target platform
which is not supposed to be supported under VS 2012.  It seems that
the behavior of VS 2012 has changed by simply installing VS 2013 alongside
it.  That's odd.

This commit contains no actual platform assembly for Windows Phone 8.1.
That's still pending.

Conceptually, I am doing something wrong by building the reference assembly
four times with four different PCL profile numbers.  But it's not clear that
there exists one profile that covers all use cases.  For now, I'm going to
let this particular insanity continue to grow.

I wonder how much people like the reflection-based platform resolver thingie.
The distinction between the "old" reflection APIs and the "new" reflection
APIs is in play.  Removing that resolver, and thus, forcing everyone to
do "SQLitePCL.Platform.Instance = new SQLitePCL.SQLite3Provider();" would
take that issue out of the equation.