The tie breaker for 5-7 teams is even more favorable to Duke than that. Only the top 5 APR teams are considered first. Last year, those 5 were Wisconsin, Northwestern, Duke, Michigan, Stanford (all hit 6+ wins anyway). Assuming it's a similar group this season, Wisconsin, Michigan and Stanford will be irrelevant again. Duke and Northwestern would be the only 5-7 teams considered at first.
The sad part is, in the extremely unlikely event that there's only one spot for a 5-7 team, Duke's loss to Northwestern head to head would probably end up costing Duke the bowl bid. It's also possible that Virginia has entered the top 5 in APR, in which case the game against Virginia could essentially be for a bowl tie breaker. It's much more likely, though, that Duke would make it to a bowl at 5-7.
Army and Virginia are must wins. Then pull out 1 of the other 5, which should have a good chance of happening. Cut's new recruiting pitch: "Duke's academic excellence will allow you to go to the Idaho Bowl even if we only have 5 wins."