I received Mary Panprase's birth certificate and the marriage certificate for Thomas Williams and Mary Penprase (notice the two spellings). I'm happy to report that the Mary noted in the 1871 census does, indeed, seem to be my great grandmother.
1871 census for Mary & family
2 Carno Street, Uchlawrcoed, Rumney, Bedwellty RG10/5329 folio 62 pg 47
William Penphase head mar 50 mason b. Cornwall
Elizabeth wife 45 b. Cornwall
William son 12 b. Monmouthshire
Grace dau 10 b. Monmouthshire
Mary A dau 7 b. Somersetshire
Richard H son 6 b. Somersetshire
John P son 2 b. Glamorgan
On the birth certificate her father, William, is listed as a journeyman mason and the mother, Elizabeth, is formerly Caddy. Mary Anne was born 7 Nov 1864 on King Street, Taunton.
The marriage certificate has some tantalizing clues about Thomas. Thomas and Mary were married in the Wesleyan Chapel 02 March 1885. Mary, 21 and a spinster, is listed as residing at Tolcarne St, Camborne; her father is William, a mason. Thomas, a Tin Miner, is listed as residing in Troon, Camborne. His father is listed as Edwin Williams, deceased, also a Tin Miner. Thomas is listed as age 33 and as a widower. His death certificate from 1898 lists the informant as his daughter Rose. Rose does not appear in the 1911 census with Mary Williams and the other children so I presume she was older and already married. Possibly she is a daughter from Thomas' earlier marriage. There is one inconsistency. The death certificate from 1898 lists Thomas' age as 50, indicating birth year of 1848. The marriage certificate from 1885 lists his age as 33, indicating a birth year of 1852.
Any suggestions for future research? Thank you for the help!