Hi John,
Thank you very much for your suggestions.
1) I actually descend from the first couple that you suggested, Pedro Moniz de Medeiros/ Afonso & Maria Vieira, who got married on November 26, 1703, in Achadinha, but from my paternal grandfather's side of the family (mostly from Salga, Achadinha and Fenais da Ajuda). Their descendants lived in the area for many generations thereafter.
2) The other ("7- Pedro Moniz de Medeiros, alferes...", RR) that you suggested, married Ana Soares de Macedo ou Dutra in 1726 and had at least one child, Maria. Hypothetically, this Pedro Moniz de Medeiros could have lost this wife within a year or two from their marriage in 1726, gotten married with Josefa da Costa soon after, and lost his second wife the next year since Josefa da Costa died in 1729. However unlikely, though, I tested this hypothesis, but I was unable to find any death record for Ana in the late 1720s. To completely rule out this Pedro, I searched for children from Pedro Moniz de Medeiros and Ana Soares de Macedo ou Dutra born in 1729 or later in Fenais da Ajuda, and indeed, they had a son named Pedro in 1730:
This Pedro is also ruled out.
In short, there were at least three contemporary men named Pedro Moniz de Medeiros living in neighbouring parishes, unsurprisingly in Fenais da Ajuda and Achadinha.
3) The Pedro Moniz de Medeiros that I was referring to first moved to Agua de Pau for his 2nd marriage with my direct ancestor and then to Santa Cruz, Lagoa, for his third marriage. I descend from the third Pedro through my maternal grandfather's side of the family, who were mostly Ribeira Grande and Lagoa. After having ruled out the other two, I really think that he was the son of Pedro Moniz de Bettencourt and Catarina de Medeiros because some of his potential siblings had the surname Moniz de Medeiros and moved to Lagoa as well around that time, but I just can't find evidence.
I have to admit defeat and accept that this is the end of the line.
Thanks!
Carlos