To combat this problem I decided to pull off only 2 points of the outer snowflake, stick them down, and then pull and stick as I went to finish putting the snowflake down on the fabric. This method worked much, much better.
In the two pictures above you can see the snowflake with and without the stitching. I love how the double blanket stitch really adds an extra design element to the applique. It also makes it look finished to me.
Here is the finished top. As I was working on the last snowflake I had a funny thing happen. I was stitching around it and I ran out of bobbin. I now know that one bobbin of Glide thread can stitch all the way around these snowflakes except for this much:
I hate it when that happens....