@jmerriam I agree with you that the "drag-and-drop" method of moving Gradebook columns is a royal pain. There should be a better way to move the columns.
That being said, I'm going to suggest to you that you not waste your time trying to organize your Gradebook. My Canvas courses have many, many graded assignments, and I never spend time moving around those columns. The only columns I move to the left, next to the students' names, are the Total, which is a percentage, and the Weighted Assignment Groups. The Total column is easy to move by clicking on the three dots. The Weighted Assignment Group columns have to be dragged over.
Once I've done that, I use the Gradebook Filters to find the grades I'm looking for. For example, I might look at the grades in one of my Assignment Groups (e.g. Weekly Quizzes, Compositions, Final Exam) or at the grades in one of my Modules (e.g. Week 1 Module, Week 2 Module). I can even choose an Assignment Group + Module (e.g. Homework Assignments in the Week 3 Module).
Using the Gradebook Filters will make your life so much easier. You'll be able to find exactly what you want without having to rearrange all of the columns.
Good luck!