Resizable and Reshapable

Does anyone know what the differences are between GoObject.Resizable
and GoObject.Reshapable? Setting just one or the other never seems to
have any effect in my code… only when I set both do the resizing
handles disappear.

That depends on the kind of object that is getting selection handles.
Reshapable only has an effect when Resizable is true.
For a plain old rectangle, not Resizable means it gets a bounding handle rather than any resize handles. Resizable and not Reshapable means it gets four resize handles, which allow the user to change the size of the shape, but not its aspect ratio. Resizable and Reshapable means it gets eight resize handles, which allow the user to change the Width and the Height independently.
You can easily play with these and other properties in Demo1, where you can interactively set things to see what happens.