OK, so after reading your post, my main and only thought was:
Why?
What is the point of what you hope to do? I'm going to turn your idea into swiss cheese here, so don't get offended - maybe it will let you consider other angles here.
1. Your timeline made me laugh out loud. No one on this board or their kids are going to be alive on this planet for your timeline of 100-200 years. Think about where this country was 200 years ago and compare it to now. Now, think about the acceleration of technology and imagine 200 years into the future. You are attempting to create the Roman Empire here, something that lasts into perpetuity, when today you're lucky if you can create something that lasts 20 years.
2. What is the societal value of driving down rents over time? The creation of some type of socialistic egalitarian society? It counteracts human nature, which is laziness, greediness, self-centeredness. Even in the nascent years of Communism, the idea was dead within 10 years; the Soviets only managed to recreate a society of oligarchs and peasants under the lip service of equality. The Chinese got a little smarter and have tried to overlay capitalism on top of it, unsuccessfully. Various other societies have more or less income and living inequality but none can counteract human nature, which is why some form of capitalism is inevitable.
3. Who is going to want to invest in a scheme of diminishing returns? You're talking about programs generally run by the government as the operator of last resort because no one else can make enough money to make it make sense. Where do you expect to receive the money to buy out your "partners" in these companies as you drive returns into the ground?
Overall, it sounds to me like you want to help the poor. If you want to help the poor, force them to learn financial management and get up and get to work. Better yet, accept the fact that there are always going to be the poor, and a good number of these people - especially in class-movable societies like the US - are going to be there because they aren't motivated enough to do anything further.