I finally discovered the answer to my question at MSDN in an article called How to: Autoload a VSPackage. The "trick" is to set the ProvideAutoLoadAttribute on the package class that's created for the project. Here is the declaration for one of the projects I am working on:
[InstalledProductRegistration("#110", "#112", "1.0", IconResourceID = 400)]
[ProvideMenuResource("Menus.ctmenu", 1)]
[ProvideAutoLoad("{f1536ef8-92ec-443c-9ed7-fdadf150da82}")]
[Guid(GuidList.guidXamlHelpmeetPkgString)]
public sealed class XamlHelpmeetPackage : Package
{ ...
The third line is all that I added to make the otherwise working extension load early rather than on demand.