1pm is safer, and I gave you the trick for immigration. The airport is a lot closer than, say the airports for Galveston.
I don't use Carnival transfers in New Orleans or most places, but Carnival does say 11:30am, so the 11:25am should be possible. If people were missing planes right and left, you would hear about it and Carnival would update the website.
You would be debarked as a Carnival tour group, so would receive some priority. maybe next time I'll try that to find out exactly what their process is, but I have a feeling you need to be ready to leave early. Personally, I prefer to take my time.
If the ship were late the flight could be a problem, but then, so could the 1pm, although you have some margin.
As for Progreso, I like it - more like real Mexico. Cozumel is more like the 51st state but with nice beaches and water.
Here are pictures from a couple of things I have done on Progreso stops....
Uxmal - one of the ruin tours
and just hanging out in town - walking around, double-decker bus, food at one of the better known restaurants...