The way I went about it was I sent an email first to the PI of interest briefly introducing myself and why I am emailing them. Then I told them I really enjoyed the work being done in "X" paper and that I have skills that are similar to what was required in that. Finally, I explained that I was trying to attend medical school and working for his/her lab and gaining pubs would help me reach that goal. Left my phone number and email address and attached my resume. I think 9 NIH PI's responded and 3 offered me an interview just based on the email I sent.
I think this is solid advice. I've had several friends get AMC roles this way. Some of them were volunteer and some were paid, but it doesn't hurt to ask. While some people might re-route you through HR, many positions take a while to get posted and by the time they do get posted the PI already might have someone in mind. As long as the work in that lab interests you, I say go for it.
Even if they do re-route you (and chances are they will as usually institutional policies will require all applications be funneled through official channels), you are on their radar. They may request to see your application even if HR doesn't forward it.
Just wanted to thank everyone, I 100% wouldn't have emailed anyone unless someone told me It was acceptable so this was a huge help.
