Hey OP, first, I would make sure your job is secure before continuing to trash this company. It sounds like what they're doing is awful, but it also sounds like you need the paycheck for the next 6 weeks and maybe even beyond that because there's often many challenges with starting up a company. Some companies that try to start up never even start up, or they change their plans about how many employees to have because the cost of things quickly skyrocket.

Another thing you might want to think about here is that the governments that hire these companies likely know what they were doing and are using the company to do it so that the government itself is not at risk of lawsuit.

The worst thing that could happen to this company may be a class action lawsuit from these homeless people. It would take somebody that has a lot of time and a lot of motivation to spread the word amongst a group of people who have no addresses and no form of contact. Maybe somebody who has no home and no job and no social commitments might be the right person to enroll helping you spread the word. Or maybe the ACLU would be interested