Missing SQLite data source in Visual Studio 2013 Express

After spending whole day of trying, installing, deinstalling I cannot help myself anymore. Maybe someone can give me a helping hand on it?

My problem: SQLite data source is missing when I try to add an item of ADO.NET Entity Data Model to a project. Yes, I did google and tried all suggestions I could find - without success :-(

My environment: Windows 7 64-bit, Visual Studio 2013 Express. I did install EF6 from NuGet (version: 6.1.3), as well as SQLite 1.0.99.0 as a bundle from SQLite page (sqlite-netFx451-setup-bundle-x86-2013-1.0.99.0.exe)

packages.config

<packages>
<package id="EntityFramework" version="6.1.3" targetFramework="net45" />
<package id="System.Data.SQLite" version="1.0.99.0" targetFramework="net45" />
<package id="System.Data.SQLite.Core" version="1.0.99.0" targetFramework="net45" />
<package id="System.Data.SQLite.EF6" version="1.0.99.0" targetFramework="net45" />
<package id="System.Data.SQLite.Linq" version="1.0.99.0" targetFramework="net45" />
</packages>

App.config

<configSections>
    <!-- For more information on Entity Framework configuration, visit http://ift.tt/1eigFsq -->
    <section name="entityFramework" type="System.Data.Entity.Internal.ConfigFile.EntityFrameworkSection, EntityFramework, Version=6.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" requirePermission="false" />
  </configSections>
  <startup>
    <supportedRuntime version="v4.0" sku=".NETFramework,Version=v4.5" />
  </startup>
  <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" />
    </DbProviderFactories>
  </system.data>
</configuration>

Thanks a lot for your advice!