I agree with every part except prison having to be a nasty place.Well, I think we're largely on the same side of the coin here. I'm not advocating rape or beatings as part of the public penal system. But the system can't be simply another public housing project where bureaucrats house people that don't care about where they are and are just as criminal inside as they are outside.
Interestingly, in the thirteenth amendment outlaws slavery except as punishment for a crime.
In short, convicted criminals can be considered slaves of the state, so compulsory labor without compensation IS constitutional.
Also, break the prisoners up into smaller lots. Rotate them occasionally to break up alliances.