I took your advice and sent out an email to the Director/Producer and offered to apprentice with him.
His emails are always scanned first by his assistant and so I received a fairly quick response that said:

“We’re not currently in production and our office staff is at full capacity, but if anything opens up I will let you know. Thanks for thinking of us.”

My husband said I was given the typical American ‘Thank you but no thanks’ response.
I don’t care if that is so. I dared. I wrote. I sent it out. No attachment.
On to the next dare…

That Screenwriter.