You probably won't pass anyone who uses a rent check system. Try private landlords and offer a substantial security deposit (3 months is good - that will keep you roughly 4 months paid ahead on your rent). Maybe try to find a room to rent in a private home. Not the best, but you can save money and rebuild your rental history.
This is a great time to buy a house. Rent a room, save your money, buy a house or condo. But there's no lease breaking then...
PS - don't sign a lease this time, go m2m.