Film is indeed a very difficult industry to get into, and I would consider taking absolutely any job within the industry, not just limiting yourself to the role of script reader.
I'd probably avoid the use of humour unless you're certain it sounds highly polished and would make them laugh with you, not at you. You have to leave them wanting more. Don't just use a generic letter – do your research. It might sound dull, but the way you communicate what you have learned from research is what makes the recruiter realise you are serious about the job. I read my university interviewers past years' papers so i could use his own interests to seduce him at interview- it worked!