I think the only way to make inroads might be to somewhat circumvent the government. Build something that has a track record of true reform, and maybe eventually hold a monopoly on prisons that actually work and serve the purpose of reform over 'penance'.
I don't know exactly how you'd organise this, I guess you want to score them by recidivism rates (and high-school diplomas?) with massive penalties for escapes / deaths etc? Unlike charter schools you could assign prisoners truly randomly, statewide, for good statistics.
No doubt there are lessons to be learned from many countries' systems. Maybe we should encourage foreign companies to enter this market. I'm personally dubious that the Nordics have some secret sauce (to adapt Milton Friedman's quip, have you heard about the Swedish-American prison gangs?) but would love to be proven wrong.
The 'bonus' could be tied to performance/behavior/etc... and it could be 'will-able'.. in case you're a lifer, or die in prison, your family will have some benefit. A lot of poverty is because the breadwinner is in prison...if the breadwinner could still win bread while in prison it might positively effect poverty quite a bit.
https://bloggingheads.tv/videos/53070
Usmani believes that something like the Nordic model would work in the US. I don't think Loury is buying any of it (and he knows quite a bit about this topic, quantitatively too) but is a model of polite, serious, engagement.