Sorry Ryan, I was wrong. The 5.x-1.7 version does fix the issue (so far ... still some more testing to do). I was troubleshooting uc_roles.module, then uc_order.module, and finally uc_cart.module. From this review I was able to connect the dots and see that the reason why it was executing the code twice was because of Workflow.

One of the core workflows provided by Ubercart had been modified a long, long time ago (before I was involved), and the action was to set the order to "Completed". Therefore the order was running through its "Completed" steps twice -- once for the core workflow, and a second time for the secondary workflow that had been modified.

I still haven't run this with production Authnet, so that will be the true test. Previously it ran successfully in test but failed when we migrated to production. I'll give an update once we have performed this step.