Hi Brian, right now your hat is made up of several independent surfaces that happen to be sitting right next to each other.
You should select these individual pieces and use Edit/Join to glue them together into a connected piece.
When surfaces are connected it will generate proper meshes that have aligned vertices along shared edges.
When surfaces are not actually connected to each other each one will get meshed individually and the mesh vertices may not perfectly align on the generated meshes, particularly when you have some large and small pieces that meet in a "T" type formation like you have here.
One surface piece may need some tuning, it has a small fold in it where it collapses down to a corner, this is the kind of thing that I was talking about the other day:
So after joining one problem will be removed.
But another problem is in your shapes:
When you zoom in to that corner circled above, you can see that it is not a flat surface as it appears at first, there is a small area where it has a bent and twisting piece in it.
That piece will need to be rebuilt with some cleaner geometry, let me know if you would like some help with that part.
It looks like some of your input curves were at some slightly different elevations with respect to each other, it would be better if these things were all lined up.
- Michael
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