System.Data.SQLite

I am trying to get ‘EF Designer from Database’ to work in Visual Studio Community 2015 with a SQLite database.  But I'm not able to see the SQLite Provider or my existing SQLite database when trying to choose a new connection.  

My VS project properties target .Net Framework 4.5.1 and Any CPU | Prefer 32-bit.  I’m on Windows 8.1 on a 64-bit computer if any of that matters.

I used NuGet Package Manager to install Entity Framework 6.1.3 and SQLite 1.0.101 (which installed System.Data.SQLite, System.Data.SQLite.Core, System.Data.SQLite.EF6, and System.Data.SQLite.Linq) in a new WinForms app.

The only Data Sources and Data Provider I’m seeing in the Choose Data Source dialog box are MS SQL Server.  

My app.config file seems to me to look OK (below), though I've seen numerous posts about previous versions of SQLite and VS that suggested different settings, many of which I've tried without success:

<entityFramework>
    <defaultConnectionFactory type="System.Data.Entity.Infrastructure.LocalDbConnectionFactory, EntityFramework">
      <parameters>
        <parameter value="mssqllocaldb"/>
      </parameters>
    </defaultConnectionFactory>
    <providers>
      <provider invariantName="System.Data.SqlClient" type="System.Data.Entity.SqlServer.SqlProviderServices, EntityFramework.SqlServer"/>
      <provider invariantName="System.Data.SQLite.EF6" type="System.Data.SQLite.EF6.SQLiteProviderServices, System.Data.SQLite.EF6"/>
    </providers>
  </entityFramework>
  <system.data>
    <DbProviderFactories>
      <remove invariant="System.Data.SQLite.EF6"/>
      <add name="SQLite Data Provider (Entity Framework 6)" invariant="System.Data.SQLite.EF6" description=".NET Framework Data Provider for SQLite (Entity Framework 6)" type="System.Data.SQLite.EF6.SQLiteProviderFactory, System.Data.SQLite.EF6"/>
      <remove invariant="System.Data.SQLite"/>
      <add name="SQLite Data Provider" invariant="System.Data.SQLite" description=".NET Framework Data Provider for SQLite" type="System.Data.SQLite.EF6.SQLiteProviderFactory, System.Data.SQLite.EF6"/>
    </DbProviderFactories>
  </system.data>

EF6 Designer Support in Visual Studio Community 2015