Do you intake anything that could potentially screw up your sleep schedule? It might not seem like much, but drinking coffee or something else caffeine-based regularly can be just enough to muck you up from naturally keeping a daylight hours schedule, where you're up at a decent time and can have access to opportunities for yourself that are only available during normal "working" hours, we'll call it.
Figuring out simple stuff with your physical health (and diet) no matter how tedious it seems, is more important than I think people want to give it credit for. You wanting to give yourself exposure therapy is a good sign. Progress is slow, and it takes time for many of us to come down off that intense "I want to do something to permanently feel better now!" feeling.
I will literally eat a whole sliced cucumber with hummus and a fairly healthy breakfast smoothie for meals, or lentil soup, etc. I drink a lot of tea and water. Fries and frozen chicken with breading might be the only "bad" thing I eat because it's cheap.
I know you've got plenty on your plate to deal with, but try to slowly work on the physical too. It can ease some of the things that can effect you mentally in small ways that eventually culminate in actual biological changes (like getting your sleep to fall into a natural day/night schedule).
I also think working on physical changes (and maybe even exercising more) are something fairly simple to focus on while you work towards larger changes with your mental health that can't always improve right away. Physical and mental health are tied to each other. If your mental health is overwhelming, learn and research on slow, sustainable physical health changes you can make in the meantime.