You're absolutely right about the job market. I've been looking for collections jobs, and they're all either unpaid or poorly paid internships or require years of experience. I apply to some of them anyway, hoping I can substitute a combination of internships as well as military experience doing leadership, management, and artillery databases for experience with collections management and databases, but I suspect there are people with the desired experience and much more of it than I have applying for the same job.
At this point, I'm applying to other jobs in other fields where my history degree is still relevant and my military experience is more highly valued. Jobs where my low experience level actually matches the job description's qualifications expectations. Once I have built experience there, I can then try to break into museums from a different angle. Hopefully I won't have forgotten all the great ideas our cohort has discussed in our various classes.
It's a different approach and it might not work but it's pretty much the only option I have, after all I need to eat and pay rent.