There used to be a working cotton press similar to that bottom one, where the mule goes 'round, at a living history place near Columbus, Georgia--but not too near, way out in the country. They've up and moved everything closer to the city of Columbus to see if they could get more traffic/visitors/money, and I've not been down there since. Would love to know if it's surviving.
I tried to look up the size of a cotton bale a while ago, to see exactly what people were talking about when they said they made so many bales per acre, and I was surprised how variable it was. If there was a legal definition of what one bale weighed, I couldn't find it.
Third paragraph, right hand side, 1853:
450 lbs:
https://books.google.com/books?id=YKIEAAAAYAAJ&pg=PA117
Left hand column, premium winners, 1853:
500 lbs.
https://books.google.com/books?id=YKIEAAAAYAAJ&pg=PA286
Right hand column, partway down, 1847:
400 lbs.
https://books.google.com/books?id=MqIKAAAAYAAJ&pg=PA69
About 2/3 way down the page, 1838:
400 lbs.
https://books.google.com/books?id=5aBH8hwd2-8C&pg=PA197
About 2/3 way down the page, 1851:
400 lbs.
https://books.google.com/books?id=oFFJAQAAMAAJ&pg=PA569
So in that short list, 400 pounds dominates, but there's also 450 pounds and 500 pounds, quite a difference.
There just seemed to be no rhyme or reason, and it apparently depended on the size of the local press. The cotton itself was surely sold in pounds, which made more sense, because a bale could be made worth more or less by baling tighter or looser. But I was surprised to see how often bales were talked about as a system of measurement: "my overseer got a bale to the acre this year," "the land is so rich it brings 2 bales to the acre," etc., which really meant nothing.