I find getting too little sleep very stressful. I'm required to keep doing the same things, but less able to handle those demands. When I don't get enough sleep, I've got worse health, constant headaches, and neck aches. It's its own stressor, as well as having separate negative effects.
Yes, but that's a specific physical stressor, resulting in mental stress. It's not what is being examined in the article and modeled in the experiment.
In practice the two will be impossible to tease apart at any rate. Stress and lack of sleep make a feedback loop. The more you feel like you're drowning, the harder it gets to find sleep. Adding nighttime feedings just throws gas on the fire.