This would be a great solution for illegal immigration and for crime in the inner cities.
Yup. Slavery is a great choice.
It isn't slavery, it is punishment and rehabilitation combined. also, they can choose prison instead. This is way better as they get church, something to do, and they produce something. A guy sitting in a cell doesn't produce anything, a guy working in a factory does.
This is simply economic exploitation, as in the old practice of convict leasing. The convict is simply offered as ultra-cheap labor. There is no effort to rehabilitate the offender through change of his behavior.
Access to religious instruction of the choice of the offender is a right in prison.