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Thanks everyone! I created another sketch, and went through the same steps I thought I went through with the original sketch. However, the new sketch was fully constrained. I gave up on the original one. I appreciate everyone's help.

Offsetting splines is one of the most brittle part of the Onshape sketcher (something it painfully shares with Solidworks).

Now that we finally get a clear indication of unconstrained sketches, I'm struck by how often I missed the end points of offset splines being unconstrained. The blue dots are practically invisible to me.

This is probably a situation where extruding as a surface or solid first and then offsetting or moving faces would work just fine.

I got it to work. Those splines really don't want to be both offset and have coincident endpoints with one another (for some reason). I used a custom feature to find the open profiles in the sketch to show the lines that Onshape doesn't think are part of a closed profile (see screens). Then I started tinkering with constraints and modifications. The simplest to do was to delete the offset constraints on the profiles. This may not be what you want! But you can immediately see that the profiles go from open to closed and the extrude then works:

You can see it here:

https://cad.onshape.com/documents/67af1f013ccc2b7712067b8f/w/5594aaee2081eeee2076622d/e/07b939bf07b96cd0047f99ad