I am not too sure whether there is any connection with the James Conway and PJ Conway you mention but it is still good to know that there were Conways in Sri Lanka during the same period as my ggf.
My paternal grandfather was not brought up by his mother at St. Michael's Road or Moor's road. He lived in both places after he was married. It was my father Chris Conway and his siblings who were brought up there.
My gf was living with his mother in Gampola and then came down to Colombo, where he married and then moved into St. Micheal's road with my gm.
My great grand mother however, I understand was a Samuel (I think this was her maiden name) and she lived with her relatives in Colombo, down the lane which adjoins Methodist College (I am not aware of the name of that road).
Would you by any chance know of these Samuels? At least this line are probably living somewhere in Colombo??
Please do let me know if you are able to gather any additional info regarding this.