Some more thoughts on slave religion as a method of control: Have this religion be not quite so powerful as a full on paternalism world, instead be one of the many tools used to enforce compliance a slave owner might want to use

Priests are very often travelling caravans, a single Master with two or three of the most brainwashed devoted slaves. They visit the more industrial operations to try and inspire the many slaves there to at best be compliant, but maybe work hard to end up like the slaves that visited them, however hollow a idea that is

>caravan visiting the slaves during their very brief rest hours
>"look at how happy we are!"
>"we spend our entire lives in servile bliss, because we accepted deep down what we were, and made sure we were the best slaves a Master could hope for!"
>"If you work really hard out in the fields you'll be rewarded too! If not in this life, then the next!"

Hard to say how effective that really would be. But it's a better thing to believe in than the reality of "do as you're told or else you'll get hurt". Depends on exactly how beaten down such a slave is honestly, it might inspire further rebellion and disobedience instead.