I tried to name this a formbuilder matrix and not a Likert widget due to the fact that it should not only support Likert scales. Ideally, the likert scale with the attributes stated by Joel would be a special case of the formbuilder matrix and make use of it in the assessment.
If you face an issue with multiple different user values depending on each question, I'd suggest to have multiple formbuilder matrix widgets, each grouping the questions and the values. Otherwise you might be better off writing the HTML code on your own (just kidding).
Alternatively (and especially true for assessment) we should handle the different scores of a value with the testing/scoring part of the assessment or the grading module, if you are keen on immediate scale results.
To be honest, I do not forsee someone using this widget in his/her package in the way you describe, except the assessment package. Therefore I'm reluctant to add scoring values to the widget itself.
