Do your PMs have a background in the type of engineering that you do?
It may be helpful to point out bad requirements whenever they're provided. Keep a copy of the bad requirements and why they're bad, so when they repeat their mistakes, you don't have to repeat yourself explaining why the requirement is bad.
I think driving towards the point of this thread, I could envision a JIRA plugin which helps writing complete and well defined stories of manageable size. It could simply be a template with appropriate sections, or a Q&A bot which drills down to the requirements.
It may be helpful to point out bad requirements whenever they're provided. Keep a copy of the bad requirements and why they're bad, so when they repeat their mistakes, you don't have to repeat yourself explaining why the requirement is bad.