Intermittent disc brake rubbing
After working on this for way to long, I think the problem is a combination of oversized dropouts and not enough tension on the quick-release. I discovered that if we stopped and loosened the quick-release while making sure that both axle ends were seated in the dropout that noise would stop.

I think what was happening is that the force applied on the disc would cause the wheel to shift a bit in the dropout and start rubbing. Each time I did this I tightened the quick-release a bit and after a few tries it seems to be resolved. I'm surprised by how much I had to tighten the quick-release. It is way tighter on this bike than on my bike which has rim brakes.