Make Use of What You Have
The corollary to changing layers when something is difficult is to use what you have when you can.
I feel like I spent the day chasing Carmen Sandiego.
Instead I'm going to randomize the options before handing them to ng-select. Underscore's _.sample function works nicely. It's already included in the project, so it can replace the homemade array shuffler. No touching the DOM outside of a view. No extra directive.