Far be it from my to cast doubts on anyone’s research but..............
There was never a ‘registar’ until the intro of Civil Registration in September of 1837, Entries made in Parish Registers previous where either by the Vicar/Curate or officiating minister, or as seems lightly in many cases the Church Warden who entered any number of events at one time.
Loveston Parish registers only cover: Christenings (1791-1977), Marriages (1783-1957), Burials (1791-1977). B.T.’s begin in 1799.
Carew Parish Registers begin in 1718 although some B.T.’s held at the NLoW start in 1685.
Mind the info could have come from the likes of Francis Green Collection who has limited entries from Haverfordwest P.R.’s for periods going back to the mid 1500’s, lucky I found one of our own ancestors there in the H’west St Mary Register for 1554. So the info may well have come from something similar.
So to answer your question no there is no mrge entry to equate to John Palmour (various spellings) for the period 1689 to the 1740’s, in the area between Loveston and Carew or any surrounding parishes, the nearest is John Palmer who mrd Jane Palmer at Amroth in 1761.