I'm enjoying reading your ideas about basic income very much. However, I think you underestimate the productive nature of human beings and the value of incentives other than survival or money.
Almost everyone I know has something productive they do outside of their paying jobs. In other words, they spend 40 hours a week working to make a living, and then they voluntarily, for no money at all, do the work that matters to them. For some this is volunteer work to help the less fortunate, others garden, sew, make things, create art. Look at all the developers working on open source projects for no pay.
In the early days of the Libyan revolution, when the protesters took Benghazi, one of the first things they did was go out and start cleaning and fixing up the city. For nothing. Because it was theirs and they wanted it to be nice.
If you don't take that part of human nature into consideration, only looking at greed and laziness, you're missing a major part of human behavior. Any systems created from those assumptions will necessarily be flawed.
I fully believe people are productive for non-finanical reasons.