Yeah, starch that sucker. Or if you make your own, definitely add some stiffening.
Well, I got my hat (from Hong Kong) and I have to say it honestly looks better quality than the Disney one, although I like the Disney lining better.
Just to add to the alteration video since it's maybe not quite clear enough...
This is roughly how much of the seam you need to open up to get the ends of the flaps free (taking a picture of something black sucks):
And then you pull the corner of each flap further through the seam until the flaps have no more wrinkles or poochiness:
The hardest part is making sure everything is lined up and also that the final edge will be straight. You'll be sewing through the lining, crown, both flaps, and band. I elected to sew by hand, since I saw only disaster by trying to keep everything sandwiched to run through the machine. By hand you can adjust as you go. I used binder clips to help hold everything.
AFTER you sew and are happy with the look, that's when you trim the extra flap material. If you do it before, you'll have no leeway if you screw up and it's harder to hold them tight.
That's pretty much it. Other than no bias tape along the edges this seems a pretty decent cap.
-Rog