You dont need a union..you need a staff with a backbone. Many hospitals have nurse practice councils, staffing effectiveness groups, etc that must be used for good purpose. Track the days and problems on paper. Have your evidence and paper trail. Complaining among your coworkers doesnt get anything fixed. I am like the poster above where we run bare minimum staff with total patient care (we draw our own labs, baths, etc) and we do just fine. If we have to triple once and a while we work together. There are much worse things out there at other hospitals where you start tripled.
Check into your state employment laws. Im not sure about Ohio, but in TX its overtime after 40hrs. So we are scheduled 3 12's and will get 8 hours of overtime if we worked a 4th day. It usually is more due to the fact we never work 12 hours it ends up being 12.5-13 depending on how long report takes. Im not sure why you need a tech with 2 patients most of the time. You cannot compare any California pay to most places in the US as they pay insanely high due to extreme costs of living. Also, you dump your money into the union from every paycheck. Also in California you pay state tax, sales tax, federal income tax, social security, medicare, etc. Im sure the difference in pay is made up by not paying the California insane tax.
Oh, and to give you a little context, midwest states and states like Oklahoma have RN's making $17-18/hr. These nurses will triple all day long in ICU, take 7-8 on medsurg, 4-5 REAL PCU with cardiac drips. So make sure you think about it when you say how horrible your job is.