I haven't looked at the blog link but my best suggestion would be to sew them on, pain in the booty but I think it would work best to make sure they stay on and you don't get glue chunks everywhere. I would deffintely use a maniquine head to stretch out the hat before you start working on it. B/c once it's stretched you might find that you need to space the flowers closer together to fill in the empty spots. I've found this out while working with FOE bands, it helps. If you don't have a maniquine head you could use something close to the size of a newborn - if you have a daughter snag one of her dolls but make sure the dolls head is standard newborn size(13in).
I was also thinking of using the top or bottom of a 2L soda bottle. More then likely I will use the top and cut off the cap part then patch the hole so I don't snag my material. I would also cut the bottle in the middle with as flat of a bottom as possible so I can set in on my craft table so I can put my cap on the top and start gluing or sewing the flowers on.
Hopefully I didn't confuse you to much with my ideas and hopefully it helps.