Hello pascoegreg
There's not much help I can give but for what it's worth here goes.
The registers for the Weld Chapel Southgate for this time frame have been transcribed and put on the LDS site 'the IGI'
Apart from that, according to Phillimore's Atlas for Middlesex, no original registers have been deposited for safe keeping at the London Metropolitan Archives or somewhere similar, they may still be with the incumbent. There 'may' be something at the Society of Genealogists.
Trying to find the parish church for this area is tricky, there is a CofE church St Andrew, but I thinks it's too young, 1904, unless it was rebuilt on an earlier church, there is a Catholic church dating to the 1860's again out of the time frame, and then there is the Weld Chapel.
I think at this time your best bet might be here
http://www.enfield.gov.uk/448/index448.htmit's a link to the archives service of Enfield council, they may be able to give you more information on where to look next or if they have any of the holdings you are looking for.
Happy hunting.
Dawn