Great idea! I'll have to try that. I actually worked on it a bit more and here's what I ended up doing.
1. Took flower apart and then glued back together
2. Glued a piece of 3/8 grosgrain ribbon to the back of the flower and weaved the ribbon through to the backside/inside of the headband
3. Then I just glued the two ends tightly together.
It looks clean and finished. So, I guess that's another way to do it. Probably not as secure at the sewing, of course, but probably a bit quicker!