You can set widgets on the Design tab, however its intended for usage on the Page tab. If you place it on the Design tab it will become a sort of 'default' widget. This will work if you use it on a new page or if you haven't adjusted any widgets on the page tab. But as soon as you adjust a widget on a page that page will get its own definition of the widgets. Its stored in an XML field so adding it via SQL won't be easy.
You could use the reset webpart but this will reset the whole page tab and has to be manually done for each page.
If your sure all pages can be reset to the default you could clear it for all pages using that template. Otherwise try it with webparts as Petar suggested.