I believe the issue is that you cannot make a widget from a webpart that INHERITS another webpart.
It's a rather annoying thing i know, i have run into it many a time (it's why you have to clone my Transformable Webpart instead of just inheriting from the base). You actually need to create a non-inheriting web part if you want to turn it into a widget.
Easy way is to just clone the web part (but not the file), and just hve 2 webparts pointing to the same file.
Unless your custom web part does indeed have it's own file, then just manually add all the inherited fields.