Hi Millie,
Yes, I've ruled them out as Price was married first to Anne Hall (1835) and then to Sophia Thomas (1844). His residence at the time of his 1844 marriage was Dowlais. He and Sophia married in the Bethesda Chapel in Dowlais, which I understand to be an Independent chapel.
There is a non-conformist baptism for a Price son of Thomas Edwards in Pembrokeshire in 1812 but none of the evidence from the censuses suggests he was from Pembrokeshire so while I haven't rule it out, nothing is pointing me in that direction (unless there was a very small religious nc community church there that the family subscibed to).