Talking about rotational approach.
No intention to comment on creativity. I liked it. It looks different. However I do feel it is somewhat over engineering. This approach works for number columns. For non number column, you would need a separate set of icons. More maintenance would be involved in this approach.
In addition, as already pointed out by a comment, the affordance needs to be re-learned. You mean well, but for a small time, user would need to make out the tiny details of your icon.
The toggle button approach has similar issues about assets, but in addition it is also consuming more space for the user. If the column width is reduced then it will be cluttered. So the solution needs some breathing space and a generous minimum width. Plus I guess there will not be a way to show an unorganized state of the column.
The problem of unorganized state icon remains. In both the approaches, you'd have to give additional affordance to show which column is being sorted. That is a visual load.
Just my two cents.