Watch out for death spirals. When you apply a penalty to everyone's actions, you make it harder for them to succeed. And when they need to succeed or the penalties get worse, failure gets more and more likely. This is amplified if the difficulty is also increasing, say because they have to take higher risk actions due to time constraints. Due to that mechanical trap, it can become much harder than it looks to turn things around.
It might be better to get rid of the penalties and keep it descriptive, similar to the way hp work in D&D, i.e. no penalties until you drop. That way you can still die of hunger, but there's no spiral. Another option is to take away some of their agency, say having to make a will check to avoid grabbing a burger, even when it's clearly a trap. That adds danger and complications, while punishing the players in a different way, because they can't do what they want all the time. Or change to a mode that's not harder or easier, just different. For instance, give them a desperation bonus for immediate physical actions, but things that require concentration or thought suffer. That will change optimal tactics, and can make it feel like a different game, which can be a fun change up.
Or just make it all about resource tracking. After all, unless they're starting out, characters in a post-apocalyptic game should be collecting resources. A home bases, allies, stashes. Give numbers to everything, and let the players build up a scorecard/treasure trove. A disastrous event like losing their base and having to flee might result in a temporary shortage, but after the first few sessions the game shouldn't be about recurrent privation. Instead, the players should be focused on the best way to use and build the resources that are available. A campaign structure designed around this would have a timeline as store shelves are stripped and goods go bad, but also options to build new resources like setting up farms, or trading for the output.