I haven't given up either.
Did you follow through on osprey's birth reference for Elizabeth Jane Williams
Sept quarter 1883 Dolgelly vol 11b 356?
Looking at the NorthWalesBMD site this is proably the equivalent of
Eliza Jane Williams,Dolgellau,Sub District Barmourth,1883-ref DOLB1/21/E158
and another of interest may be
Lizzie Williams,Dolgellau,Sub District Talyllyn,1885-ref DOLB2/16/E306
(These are the references the local office may use)
Whether they would tell you if either had a mother Sophia,a father Evan(or both!) or any other detail by phone or e-mail I can't say.
General enquiries to the County Council are here(including an e-mail form)
http://www.gwynedd.gov.uk/gwy_doc.asp?cat=5526&doc=19116&Language=1&p=1&c=1General telepone number is 01766 771000,and I think the number at the Registry Office,Cae Penarlag may be 01341 424386
Regards
Roger