You could contact emergency housing in your area and explain your situation. Not that you are looking for emergency housing, but since you do face barriers to finding housing, they may know where you can go. If that does not pan out, try contacting local rental realtors (not something online) as they might know which places do not require certain amount of income to rent. Beyond that, perhaps just keeping an eye out for for rent signs posted.

If you can get a great reference from your current landlord, that does go a long way since it shows your ability to pay rent on time.

Personally, I hate how housing has become and how utterly ridiculous it has become just to find a place to live. Good luck