I left them upright. It didn't seem to hurt anything. I did notice that whenever someone was "almost out" then whoever was already hatched rushed over to crowd them. Had they been on their sides, the pipping eggs would have rolled all over. BUT the crowd support could have possibly assisted a side hatched, instead of occasionally hindering an upright one.
I missed the first one, but I watched all the others. Very fascinating. After the initial pip yesterday (that lasted FOREVER), the first chick was probably only minutes old when I found it at 6:45 this morning. The other five had hatched by 11 or so. That sounds slow, but it was like popcorn.
I had put paper towels and a washcloth on the wire mesh, but they kept climbing back into the cartons. That's the biggest reason I moved them; they seemed to be having trouble maneuvering the wire and cartons, and I wanted them to get their legs straight. Also, I didn't want them bothering those last three eggs, in case I have another rotten one on my hands.
Here they are all dry:
Perfectly adorable picture!
I'm just gonna hop on back on here so shove over. 
