I know this is last minute but I wanted to put this out in hopes it may be of some value to one of the readers.
Last year my daughter, son and I had tickets to the Easter Vigil at St Peters conducted by the Pope and it was truly the highlight of our trip.
Now true we wrote to the Prefecture of the Papal Household well in advance and while in line, many people came up asking if anyone had extra tickets.
One of the people suggested that there might be remaining tickets and sure enough, a young couple went and came back with tickets and said there were many unclaimed ones still in the office.
I do not remember the name of the particular office and perhaps someone reading this will know the official name, but I do remember that as I was facing St Peters, it was on the right side at the start of the columns. There was a police check point but they were very friendly and it seemed they allowed people to check for last minute tickets.