I graduated in 1992 during a mild economic decline, especially in California. Six months later, still no job. So I took my act on the road. I also thought it important to kick start my career with a proper internship at a teaching hospital. That helped limit my job search. So I called every teaching hospital in the country, well just the ones with toll free numbers (a very different era), and drove across the country, stopping in every city that agreed to interview me. After perhaps 10 interviews, I finally snagged a job offer in Baltimore of all places. Worked there happily for three years and have been traveling ever since.
The 8 month orientation and subsequent experience served me well for I've been able to take what the next 40 highly varied hospitals have tossed my way.
The confetti method of looking for work the way you've done seldom works. Pick your targets and follow through. Not necessarily my approach, but you need to get through to a hiring manager. Take a few chances and cold call a manager where you'd like to work and tell them why (skip HR).