Creating a planar surface from a 2d curve results in strange unfilled geometry
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 From:  quat
10842.4 
That makes so much more sense now. Thank you!

Also, regarding the issues I was having with the geometry itself:
Taking a break and looking at it again made me realize that I had managed to repeat the same mistake each time I made the shape. I'd accidentally made the rounded front curve just barely non-tangential to the bottom surface, which made it stick out on the bottom a tiny bit. This seems to be what was causing the trouble.

Again, thank you for clearing this simple issue up. This forum is a life saver.
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