Hi Dianna,
Until 1 March 1856, there was NO requirement by the civil authorities for baptism, burial or marriage records to actual record the NAMES of the people involved. Also the civil authorities did NOT impose any compulsory requirements as to the church authorities KEEPING their own records. So any denomination and any other faith (Sydney Town was not just for Church folk, there were Muslims, Pagans, Jews, and other faiths, and even those 'without'...

The NSW BDM Early Church Records (those with "V" as part of their reference number) have NEVER EVER promoted themselves as being the complete set of bdms for that pre civil registration era.
We also need to accept that there are flaws in the NSW BDM online index and that it has been mis-understood by some of the commercial websites who have attempted to merge various versions of puterised datasets across the different NSW sets of records and added the datasets from each of the other British Colonies that became one colony - Australia - in 1901.
The person responsible for seeing that the £100 set aside from Michael's probate for his own entombment - ummm - Catholic burial ground - well it may have been Devonshire Street, but you could double check by approaching St Marys Cathedral ARCHIVIST who may need some time to check if there could be a vault in or about St Marys itself. Likely you may need to help fund that depth of research. I am sure that the archivist would need copy of the probate record and the likely date -month and year or at least year- for Michael's death.
JM