At this point, I do not believe this is possible; I believe that government should have a heavy hand in this operation, I think that if need be government should raise taxes to force its citizens into giving money, whether they want to or not.
It's not circumstantial that the essay where you take some of your inspiration was written in 1971. Over the last thirty years we have had the opportunity to see how well this kind of idea works.
In 1971, it wasn't clear that the social engineering of the USSR would not work. The biggest concern was still "what if it actually works?" Unbeknownst to the people spreading that fear, the truth about much of the USSR wouldn't come out for years. Its closed society was able to hide the fact that Stalin had killed more of his own citizens than Hitler. That there was a class system. That a large amount of their food was produced and distributed by a street-level free economy, permitted by the government because it prevented the country from starving. From 1989 on, when glasnost started to kick in, we learned that the very worst of the paranoid right's delusions about the Soviets was true.
When studying government, the biggest question should be "How can we prevent the government from going nuts and killing off a tenth of the poopulation?" The answer to this question, in my opinion, is to make government accountable to, and LESS POWERFUL THAN, the citizenry. The government cannot have power. The real power has to be in the hands of the citizens.
The government with the power to tax Peter to help Paul also has the power to enslave or kill either or both of them.
Back to 1971. 1971 was the last year that people had a broad belief that their elected officials were acting selflessly to benefit the country. A year later, Watergate broke; two years later, the Nixon tapes were released; and a country pulled the wool back from its eyes and saw that politicians were in fact politicians, not an elite group to architect solutions that would benefit us all.
But by then the political solutions were in place. A few years earlier, the War on Poverty had been kicked off - which would increase social spending to levels higher than defense, without having much effect on poverty. After two decades of this, people with their eyes open would note that 67% of social spending didn't even make it to the needy; it was eaten up by the government bureaucracies involved. You were saying that the government should take over the roles of private charity?
Look around you. The richest and most powerful nations on earth are the nations that are the most free. Do you think this happened by accident? Because it would be a pretty amazing coincidence.
If you honestly care about the poor, give them freedom. The role of the government is to provide an infrastructure of laws and systems where the free people can work and trade. At first, its goal should be to prevent fraud. Later, if it is powerful enough, the government can consider tighter definitions of fraud including regulatory approaches.
The role of the government is not to use force to coerce the citizens to do things they don't want to do. Government solutions, by their very nature, MUST be political. The power goes where the money flows, and undistributed power is not pretty, and does not worship at the same house of compassion where you worship.
If you are still registering for spring semester classes, I recommend one in 20th century history. I didn't take history when I was in college, and this has been one of my greatest regrets. People who study history have an understanding of the world beyond yours and mine.