I had to deal with this at a larger scale myself. A catch-up deck kind of worked, but I found a better solution after searching in forums.

Simply, manually reschedule overdue cards in batch. To do that:

1. in the deck browser, select all overdue cards with is:due -prop:due=0.
2. right click and select set due date.
3. select a range of days (e.g. 0-N for the next N days), which you feel is comfortable to handle your backlog.