Based upon what you've posted there are only a couple options I can think of.
Use the Width Tool and add more width markers to control areas of the path you wish to control. The goal of the width tool is to create a smooth transition between varied widths. So, yes, a large increase on one side of a marker will result in some decrease on the other side of the marker. The tool is keeping the curve smooth. If you do not want smooth curves, you need to use more width markers to indicate the actual widths you want. Note you can double-click a width marker with the Width Tool to set a precise size to the marker.
Expand your paths to shapes and alter the shapes. This is how things were done prior to the Width Tool being introduced, and I'd hazard a guess how many calligraphers building fonts work. Most type characters are shapes, not paths. While it may seem more helpful to keep everything as a path, if you want to adjust things beyond the capabilities of a path, you simply need to expand the path to a shape. If exact precision is needed, few "path altering" tools will provide that whereas it can easily be done with shapes.
Brushes may work, but will offer the least amount of control over appearance and from reading your question, that clearly won't be sufficient for you.