I have been able to move fairly easily between the non-profit, government, and corporate spheres over the past 20 years. You mentioned not understanding acronyms--it is critical to learn the vocabulary. The underlying principles and the skills required in all of these jobs are often very similar or at least translate, but the vocabulary is different and you need to use the right words to instill confidence in people that you know what you're doing.
I don't think having a degree that differs from your experience is a problem--that describes most Americans in my experience. Just figure out a one-liner to explain it, "I got my Masters in social work because I wanted to...then I discovered that my real passion was for..." Or, even better, an explanation for why your combination of a social work degree and research/evaluation experience makes you uniquely qualified for the position.
I do find that various sectors and industries often think you have to have industry experience in order to add value. That just means we trade employee back and forth, every company looks like every other one, and true innovation is less likely. I would LOVE to see more hiring from outside our industry, and if you can find a way to talk about that as a positive, not a negative, that would help. It also helps if you can talk intelligently about the sector or industry and how it's similar or different to where you've been working. Draw parallels, "Though we are publicly funded, it comes down to being able to get the best academics, which draw the best students, and at the end of the day, our students are our clients. So even though it's not the same, I do understand the need to remain competitive, build your brand, and hire the best people." (Would need to change for the type of job you're going for.)
I also want to second the advice to network, and ask people's advice. "If I wanted to make the transition from x to y, what advice would you have for me?"
If your hours do get cut to 20, would that leave time for you to do small consulting projects in the industry you want to move to? I have found that to be a great way to get your foot in the door and sometimes, a job offer will follow. At the very least, it helps teach you the vocabulary and put relevant experience on your resume.
Best of luck if you do decide to make this transition--it must be difficult to think of leaving a place where you've been so happy.