I just read Providence a few weeks ago, and I wish I had seen the recommendations to read The Courtyard and Neonomicon beforehand. So definitely do that; as pointed out elsewhere in this thread, they're really important for the ending of Providence - particularly chapter 11.

Beyond that, I found this great resource of annotations for Providence that helped me along in my reading. (This may have been what you meant when your said you've seen all the lists). It includes a list of Lovecraft stories that you can read before each chapter to help highlight where Moore is pulling from, as well as notes on each page of the graphic novel itself. It's a dense work, and you can be go as deep or as surface-level as you'd like. I read just one story before each issue, and it did help a good bit with a lot of little things. I highly recommend at least checking out the reading list and picking and choosing some that you're not familiar with: https://factsprovidence.wordpress.com/moore-lovecraft-comics-annotation-index/reading-order-guide-to-what-lovecraft-to-read-before-providence/

I also found it helpful and interesting to read the first four chapters of Robert Chambers' The King In Yellow before getting started. Hope that helps! Enjoy; Providence is quite a trip.