I have been out of the job market for a while, been working for the same company since 2002, but when I was looking I would get up in the morning and go knock on offices and warehouses and ask if they had a vacancy. Got many no's but also got yes'es.
About the agencies not allowing you to sign up for anyone else, that is bull***, I would say yes, then do whatever I needed to get a position.
At one time I was registered at two agencies and would take whatever work they had.
Also check the yellow pages for distribution companies, event organizers and hotels, check security companies and restaurants, even Pizza Hut and the like.
Cleaning, that usually is also a quick way to get money.