srksphillips,
Wherever you wish to define/change the Width, you need an Anchor Point. I believe you can (Smart Guides being your friends):
1) Create an Anchor Point at each spot where you wish to have a specific width, such as the starts and ends of the thickest parts, you probably have them already;
2) Use the Add Anchor Point Tool on the thick side right next to each existing Anchor Point (from 1)), and set the same Width;
3) Use the Direct Selection Tool and ClickDrag the Anchor Point from 2) to coincide with the Anchor Point from 1).
And the same for the thinner/thinnest part(s).
That is basically the same way as when you create a gradient with hard stops, such as a two colour fill in one object.