how do I explain the shortcomings in my work to a future employer when
they ask me for details? The honest answer would be that it was a
result of bad management – I can't lie to them, but I can't point
You are correct - don't point fingers. Just saying "bad management" would make a potential employer wonder what "bad" means to you and if you would conclude the same about them.
Instead, focus on why this company is "no longer a good fit" for you.
You can point out why being shorthanded caused problems. You can talk about the impact of being forced to cut corners.
You may want to tread lightly on the "over-worked" aspect, if you feel you must bring it up at all. It's a short drive from saying "I'm over-worked" to being considered a whiner or someone who simply doesn't want to work hard (even if you are over-worked by a lot).
If you are working 80 hours a week or such, you might want to talk about work/life balance but in general that's a phrase to avoid. Instead, ask questions about the working culture and see if you can get a sense if the pace, volume and intensity of the work meet your needs.
In general when asked, talk about some of the problems you encounter without blaming management. Any interviewer with a clue will understand how those problems came about (it's virtually always about management) without being told.
Be ready to answer the inevitable question: "So then why did you stick around for x months?" Perhaps you wanted to work hard and try to see if things changed for the better, but have only recently concluded that your efforts were futile.