-Another thought regarding Reordering... what if you leave the UI as is but make it so that clicking on another menu item causes the user to stop Reordering? Effectively, doing something other than Reordering causes the current order to save.

For example, click Reorder, move things around, then click on Summary/Education/etc to finish Reordering. Could also click on Resume (at the top) to finish Reordering.

What I like about this approach is that it removes a click from the workflow.

-Another idea would be to make double-clicking into a content block finish Reordering, and then enter the edit mode, e.g dbl-click to edit text for a job.

Just some ideas... Best of luck.