I found a thesis that sounds relevant to your questions in general, here are its details and abstract:

Prison labour for private corporations: The impact of human rights
by Vanessa Thalmann ISBN 9780494126868, 0494126868
McGill University (Canada), ProQuest, UMI Dissertations Publishing, 2005.

In the past two decades, the prison population has increased considerably in many industrialized countries. In the United States, for example, the prison population has more than quadrupled since 1980. As a response to the considerable incarceration costs, the number of private prisons and the number of prisoners working for private corporations have increased significantly. Proponents of private sector involvement in prison industries argue that inmate labour can reduce the incarceration costs and contribute to rehabilitation of prisoners.

The question of private sector involvement in prison facilities raises significant concerns as regards to international labour standards. Opponents of private sector involvement argue that private hiring of prison labour can involve exploitation. They also argue that the authority for punishment is a core governmental function that cannot be delegated to the private sector. Furthermore, in most cases, labour and social security laws are not applied to inmates. Therefore, prison labour can constitute unfair competition with free labour or even go as far as to replace free labour.

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While not mentioning Oklahoma in the section that I was able to skim (I only had access to 22 pages of it through my library account), this thesis seems to cover many of the issues you are concerned with. To actually read the thesis in full, I suggest possibly requesting it to your local branch of the New York Public Library through inter-library loan (or maybe you will have access to it online with an NYC library card if you are fortunate).

Forced labor has a specific definition which I found in the above thesis. According to Article I of the Forced Labour Convention No. 29, 1930 ratified by 177 countries as of 2013 (but still excluding the US), forced labor is defined as "all work or service which is extracted from any person under menace of any penalty and for which the said person has not offered himself voluntarily." I have yet to find if forced labor is implemented in Oklahoma prisons.

I will continue to look for freely available online resources that may have the information you need, but this was the one major find I have had in my searching up until now.