Sharon and I spent part of this afternoon talking with Roger Walters at St Mark’s. He is very much involved in the churches past, but they have few records before the mid 1800’s! We both agreed that Anna Stuyvesant was our connection to St Mark’s. The Jay Vault was probably in the Stuyvesant Orchard which is now 11th Street, and this is the reason it was moved to Rye.
The church is charming, with a very active rector and growth. Service is in the round. Nice place to visit!
Addendum. I found a map from 1815 that shows St Mark’s on the corner of 11th St and second Ave with St Marks Cemetery across second Ave. The Cemetery has disappeared and that must have been where the Jay Family Vault was.