What industry are you in? I would first review both the Nurse Practice Act and the practice act for Paramedics. In the states I practice in Paramedics cannot do Audiograms or PFT's. I don't have time to look this up - anybody who knows jump in- I don't know if PFT and hearing testing by allied health professionals meet OSHA standards.
Since they are not independent practitioners they usually must work under a Medical Director who is on duty. Do you have a Medical Director on duty when they are?
These people have the same personality as fireman. I found it can be a dominance issue. I would suggest if you can challenge both your states EMT and Paramedic exam which many states allow RN's to challenge the exam. (What you will need to get experience with is the use of the equipment in the field, like back boarding.) If you are also certified as an EMT/Paramedic they will have nothing about skill level to complain about plus you will outrank them in the field with a Paramedic/RN designation.
Next ,if they are spending so much time being paid and not working, why don't you document and suggest reductions in force for additional corporate savings.
What is your chain of command? Is your company a single site? Are there other sites using the same staffing structure?