Michael Moore (FMFFFF)

[Sue from Southend]

Name - Michael Moore
Date and place of birth - possibly 19 Oct 1754, London
Names of parents - possibly Joseph Moore and Ann (mn unknown)
Date and place of baptism - possibly 26 Oct 1754, St Giles Cripplegate, London
Details of each of his or her marriages - possibly Elizabeth Mercer, 17 Sep 1775, St Giles Cripplegate, London
Occupation(s) - Watch maker/finisher
Addresses where they lived
Shoreditch area, London/Middlesex
Date, place and cause of death - possibly 1822, John's Row, Shoreditch
Date and place of burial - possibly 6 Jan 1822, St Luke's, Old Street
Details of will / administration of their estate - none found
Memorial inscription - if any

I would like some opinions about the baptisms of Michael and Elizabeth's children please. There are four baptisms to a Michael and Elizabeth Moore, watchmaker at St Luke's Old St, 1778, 1782, 1784 and 1788.
There are another three at St Leonard's Shoreditch to a Michael and Elisabeth(neighbouring parish) in 1776, 1780 and 1787. These do not state father's occ but give place of abode which is different each time. Would you agree that these are all the same family? There's no other obvious marriage between a Michael Moore and and Elizabeth in the right time frame. The earliest baptism is for a Joseph Michael which would fit with the possible father of Michael but am I trying too hard to make it work?