They could still compete with Nike if the championships were a week apart. Most teams (especially outside the NE) aren't going to send their kids on 2 consecutive weekend trips anyway. And if some of the very top athletes faced each other 2 weeks in a row, both meets would get at least as much publicity as when the athletes have had to choose and each meet has featured only half of them.
They could also move the meet a week earlier instead of later, if there are concerns about getting too close to outdoor season.