I glanced at the version posted by Amergin in 2002, and I thought, "Boy, that's a long song!" But actually it isn't. The lyrics print the chorus every time, and the chorus has the same line twice.

I suspect somebody merged two broadsides in it. One broadside talked about barley and the seasons, The other broadside sang of barley and a man's life. If I were singing this to listeners, I would pick one theme or the other.   

Little stuff: I think "rout" is correct. A rout is a mob of fleeing soldiers, but I think here is it a playful term meaning "you fellows."
I like the sound of "come out, ye rout"

I agree that that the stubble should be wheaten. I looked up wheat growing, and whether it is planted in the spring or in the fall, wheat is harvested before September.

The barley should be hanging down its head, not it's head.
The baby should be on the breast, not in the breast.

I don't like "smiling on the scythe," but I'm not sure what to do about it.