So you don't want to give money to the people who currently are not gettinga any? You just want to discurage people who are getting money by ordering them to do some work?
Where do you get money to pay people to organize the job and supervise that it's actually done? How do you treat people who don't do the job right? Do you deny them the money and the job? Do you put them in jail? Communist states did that.
What do you plan to do about people who won't take the money if they have to lose third of their time for it?
Do you give those people money/food/shelter for free or do you let them starve or freeze?
I believe your idea is incredibly complicated in detail. I like the idea of basic income because there's so little that can go wrong. The only proble I see is that rent could just go up and suck almost all basic income into pockets of property owners.
This solves the perverse incentives created by a Basic Income and costs a lot less (you only give it to some people instead of giving to everyone).