I love to respond to questions by relating some of my experience... and I'm not saying that I have a lot of experience, just that I've had some hatches that relate to the topic at hand. On my first hatch, my first pip was the last one to hatch. The other chicks were playing kick ball with that egg. Finally, I took that egg, and put it in a little tupperware container that had the sides tall enough that the other chicks couldn't jump in. That little one zipped and was out within 1/2 hour!
My next to last hatch: I think there were 25 going into lock down. They were in cartons until lock down, and were then placed flat. I hatched 19, one malpositioned chick died after a partial assist. Eggtopsy revealed a lot of wet chicks, never pipped, and some malpositioned.
So, the following hatch: I set 26. 23 went to lock down. Humidity ran too high during the first 2 weeks, and air cells were not big enough to make me happy. So, i ran dry right up until the internal pips, then cranked the humidity up. These eggs had been flat until lock down, and were then set upright in cartons. Best hatch ever.
As much as I would like to advocate for putting eggs flat for hatch, I think these experiences point me in the direction of continuing to use egg cartons for at least lock down.