Sometimes You Just Can't Follow Their Advice

"Cover letters should never include the salutations "To Whom It May Concern," "Dear Hiring Partner," or "Dear Sir or Madam.""

I would really like to follow that piece of advice. I understand the reasoning behind it. However when the only contact information you have is a generic human resources email address it makes it difficult to follow that advice. I've looked all over their website to see if I could find out the name of their Human Resources Director, but it does not appear to be available on a public website. I know who it used to be 10 months ago, but that is no guarantee the same person is still in that position. Go with generic greeting or go with a possibly incorrect greeting, which is preferable?

I've also noticed how difficult it is to write a cover letter when six positions are open and you're interested in three of them. I need something more professional than "Hi, any of these three positions sound good to me."

Have I mentioned how much I hate job hunting?