actually, the game is possible to beat without choosing the whore path. You simply need to upgrade one of Shumma's skills that increases his income from working at the grocery store, and to do so, you will have to work every single day with no exceptions, even if you have the skill to its full level. You can access the skill through clicking on Shumma's profile and clicking the green arrow button. Afterwards, scroll down, and you should see the upgrade option in which there is a money icon on the top right corner with Lucy visible in the picture of the option. As to Rei, try getting rent from her shortly after she gets her salary to stop her from spending money on her cigarette, or you could just buy two cup noodles and eat one without her, and then wait for her to eat the other on her own in the morning, as from what I have experienced, she will actually cook for herself if there is food available and when she is hungry. And if there is no food in the fridge, she will even take your money to purchase food for herself to cook and eat. Though the condition to that happening is that you have to have money, so it's all actually a cycle of nonstop working regardless of anything else happening. You just gotta keep up the grind is all, as unfortunate as such a reality is.
Still better than forcing a girl you just saved from the streets into prostitution, though. That's just making things even worse than when she was homeless.