I haven’t been to the Dept of Records. I’ve used the online indexes you mentioned and ordered from them or (prior to last December) used the FamilySearch photo duplication service quoting numbers. I have also paid for searches and would have thought they would be able to see any mistakes/omissions at their end given that I had date of death, date of burial, address, etc ???
As for Calvary, I paid for and received an interment list back in 2000 - family plot of 2 graves. Now I know from this list that it contains errors regarding some of the family members buried there, minor stuff really - a couple of incorrect ages, the odd double LL spelling of surname. However Calvary’s information matches what is on the death certificates so you’d assume that Calvary’s information must have come from the certificates in the first place.
Mary’s interment information was given as Mary A. O'Neil, June 16, 1916, age 81. This information is correct for age and spelling so the certificate must match this if you assume the above?
I was in NYC in May last year and did a tour of the ‘old’ family haunts and went to Calvary. I ordered another interment list (a grave with 19 people - it cost me $180.00) but I asked about Mary and where Calvary would have got their info from and could they help with working backwards. The response was I need a name and a year and month of burial. I gave the person that and I was given the location, grave and plot number - that’s it! I said I could have told them that without asking, it’s help tracking the death certificate I was after. The response was to try the Dept of Records. I felt like I was on a circular path and thought cheers - I’ve come a long way and just spent $180.00.
So you see when I said I've tried everything I wasn't lying.