It's one of the reasons people push for UBI. Welfare programs waste a lot of money trying to make sure the "right" people are getting it; UBI just gets rid of the waste.
The solution is simply: Make school lunch free for every student.
Outputs would change from bool to float between 0-1. That much is relatively easy given a calculator.
They just go off of last year's 1040, with overrides for "now a thing happened" - like job loss this year when you made a good amount last year.
I think steep gradients are OK, as long as they are not over 100%. When someone is working and earning very little, they need all the help they can get. As they earn more, they need less help, and should start to shift to instead contributing to helping others. There is probably some ideal "ramp" that provides the right set of incentives. I think 75% is probably too high.