I think your willingness to work even the bad shifts to get your foot in the door will set you apart.
Apply to the jobs anyway, especially if they "prefer" experience or want less than two years.
Also look at a lot of nursing staffing agencies. Even if their ads say experience, they have an obligation to fill these spots according for contracts and business, so they are more likely to accept candidates who don't fit perfectly and/or they'll know of a position with their contracted companies that didn't require experience.
Indeed.com is a great job search site, but I posted a few positions in Cincinnati that either didn't specify experience, or only wanted one year, just to help out a bit Job 1 Job 2 Job 3
Don't get too fazed by experience preferred or required - apply and cross your fingers, interview well, and let your enthusiasm help you get the job!