Hey @chrisbog! Thanks for the clear description of your question.
Since you’ve already specified Days of Week = Friday, OmniFocus knows that the task should only be scheduled for Fridays. I think it might work out if you switch “Repeat From This Item’s” from “Assigned Dates” to “Completion.”
To test this, I set up something close to your description:
A new Inbox item, due on Friday September 21 (overdue)
Repeating weekly, on Fridays, from completion
This item is a couple weeks overdue (just like your backup task), and when I check it off, it gets scheduled again for Friday October 5 — this upcoming Friday. It skipped September 28 completely.
Hope this works for you, and thanks for using OmniFocus!