Brief Update:
So, I typo'd on the subject - RFE not RFI
Despite advice on this thread saying otherwise and at least in the State of NY - I was not entitled to apply for a copy of my deceased father's birth certificate without a court's approval. To do this, I had to get a copy of his death certificate. I was able to get this and the court order, but the birth certificate was not received before the due date. Instead I found the requirements to qualify for citizenship through a parent, and it states that he would have had to have resided in the US for 5+ years and two of those needed to be after the age of 14. My father was born in the US and left 4 years later. I wrote this in a cover letter, included a PDF of this information from USCIS' website, and then sent mail receipts of the progress made to get the evidence they were asking for. I was able to get a picture of my dad's marriage certificate, but without my mom's cooperation (it took convincing), this is also something I am not entitled to if either person is alive and doesn't give consent.
I am still waiting for a Tier II to call me back (was told 3 days, then emailed that it would be 10 days, and 30 days later I have not heard anything). I also had a consult with a Lawyer who said there was nothing a lawyer could do either other than submit the evidence for me, they did agree on the requirements and said best case scenario is they just proceed with the N400 and worst case was that they denied me in which they would then take my case if I wanted as I likely also be denied trying to seek citizenship through my father as he doesn't meet the requirements
On top of this, I waited until the due date to submit things as I was missing the birth certificate and when I logged in at 6AM that day, it said the RFE timeline had expired. I called and the person I spoke with said their system didn't show it has expired or that I missed the deadline... so just a little extra stress to add into the mix. I was only able to submit the evidence as "unsolicited documentation". I don't know if that will impact anything, but if I ever get that call back from the Tier II rep, I'll ask.