Searching for information about how to create some custom project and solution templates for Visual Studio, I came across this article - Visual Studio 2005: Create Reusable Project And Item Templates For Your Development Team -- MSDN Magazine, January 2006.
I'd presumed that I'd need to make use of the Visual Studio SDK to do this, but I was pleasantly surprised to discover that half the work is already built in to Visual Studio itself!
I'd apparently overlooked the "Export Template.." item in the File menu, but this can create a template for a Project Item (eg. a custom file) or a Project as a whole.
I then started reading the Visual Studio Templates section of the MSDN Library to see how you can create multi-project templates which I think should allow me to package up a whole solution as a template with multiple projects.