Have they ever considered running a few coaching sessions for staff? I suspect the answer is no because they don't believe they have a problem, but that's my bias from university in UK.

I am not a good speaker, but one time my employer offered an hour long session with a coach before a conference. I presented my material (something they strongly emphasised) and he was able to give me advice on getting rid of the "umms" and sound a bit more engaging. It made a big difference to what people have to listen to and gave me a confidence boost.