Josey rarely screams just some loud calls now and then but she can do a great sun conure scream. Now my sun does occasionally scream while on my shoulder and it is ear splitting if she is right at my ear when she does it, I think it too is in response to something she hears or sees outside that she feels like she has to "warn" me of, what we put up with for them.
If I tried ear muffs I am sure both of them would freak and not be on my shoulder, maybe you can try them earplugs, they are pliable so you can scrunch them up and put them in and they expand to close up the ear canal, my hubby uses them at work.