I guess I wish the positions I applied for had hiring managers as open as you are. To be honest, with the majority of the places I've applied to, I get no response at all.
Got to watch out for the HR filter. Often at bigger companies, hiring managers don't even see a resume unless it meets the criteria they specify on it. That means people like you with related, but different experience get cut out when you could still be a good match. Broken system.
Networking helps here. I've never gotten a job where my resume had to be filtered through HR first. You need to know someone who is or knows a hiring manager. Get out there and make friends!
echoing what mlitchard said. Networking is a big help. Besides that, look at what is on the job posting. Try to use the same key words in your resume/cover letter. Not sure how well it would work, but addressing differences in the cover letter could work to get it past the HR and into the manger's hands.