I crochet and I find it very interesting that almost all the doilies are sewed on upside down. Doilies by there very nature are not a tight project. A long armer would have a nightmare trying to keep those threads down & in place, and not getting hung up on the hopping foot. I would put them on after the item is quilted. It will take a lot of stitches to keep them from sagging & moving around on the finished item. These doilies that they used are done in a circular pattern. Stitching them down that way would probably work the best. That way you would be supporting the main framework similar to the crochet pattern. But, on the other hand, radiating out like with a sun's rays might actually work better.
This might help. These are directions from the same website that you referenced:
http://www.vanessachristenson.com/20...lies-onto.html