Custom Site Template missing web parts

I have a SharePoint 2013 question: I've created a page using the out of the box "Task" list app. On the page, I have placed 2 different web parts with different views of the "Task" app. the first view is the default "All Tasks" view. The second view is the "Calendar" view of tasks. On the page, they complement each other nicely, showing simultaneous views of tasks in different formats.

Now, I made a site template based on the site containing this page. When I create a new site based on this saved template, and then go to the task page, only the first web part with the default view is there. The calendar view is missing.

I've tried with other views (ghantt, etc.) but always the first view lives on, while the other views on that page get stripped off when I create the site template.

Has anyone had experience with this anomoly? I know you can switch views so there's a work around, but I'd like to have a page with multiple views going at once, without having to manually add them whenever I use the custom site template.

thanks, Doug H