Thanks for the timeline info. I've not found any likely immigrant listings other than the ones you mention.
I have found this family on the 1841, who might be worth following up:
Pen y Bryn Mawr, Llanrhaeadr YM, Montgomeryshire
John Davies, 65, Ag Lab
David , 25, Ag Lab
John , 3,
David, 2
Elizabeth, 1
All b. Montgomeryshire apart from David senior.
The entry is split over two pages - John, jnr, is on
HO107 Piece 1435 Book 6 Folio 42 Page 11
My theory, for what it's worth. is that Elizabeth died after the birth of Elizabeth, jnr.
I'll check the parish records for burials and births for this family.
Gadget