VSIX - How to create a C++ template project and include it in a VSIX project?

I am aware of how to export a C++ project as a template and then add that zipped file to a VSIX project. However I would like to add the C++ project to the VSIX project directly using the same mechanism as described here (mainly due to ongoing changes being made to the template project).

However that only seems to be possible with a C# project. With the C++ project, I get the error:

error MSB4057: The target "TemplateProjectOutputGroup" does not exist in the project.

According to this post here, the VSIX project requires an MSBuild target called "TemplateProjectOutputGroup". However I tried changing various properties in the C++ project to "TemplateProjectOutputGroup" but I still get the error.

Is there a way to make this work with a C++ project?