I don't have any experience with the HSI/HBCU/Tribal specific applications. However, and this may seem like a dumb question, have you tried talking with the Program Officer at NEH? If not I highly recommend it - they are often a treasure trove of information and I have only ever encountered one that was not pleasant (and that was a different agency).
Does your Sponsored Programs office have any advice? If you are at a small school without one, drop me a PM and I'll send you some resources.
NEH is pretty open about who receives what grants. You could also get a list of the recent recipients and contact some of those people. I find researchers in the humanities are very open to discussing their experiences with others outside their institution. The place to search all previous awardees is here: https://securegrants.neh.gov/publicquery/main.aspx