Thanks for your research, unfortunate that a connection couldn't be made there.
I think that the Goodman Jones family who were in Corwen/Chester/Liverpool/Birkenhead seem the most likely that could be related, especially as Sarah was the name of the wife and sister of John (b.1847). Their father I estimate would be born around 1820(?) and then their parents would have been John and Anne from Llangollen. I can't see an immediate obvious link between Sarah Goodman Jones and my Jones family, although perhaps they were not related at all?
To go back later a few generation, I wonder if Margaret (born in Corwen 1863) who married Henry Edward Jones, could perhaps be a distant cousin. Her parents were Robert Peake (b.1836 Corwen) and Martha Thomas (b.1839 Corwen). Robert was the son of Evan (b.1801) and Mary Ellis (b.1804 Llandagla). Martha the daughter of Evan Thomas (b.1797 Corwen) and Margaret Thomas (b.1817 Cerrigydruidion). Peake is an unusual surname in the area and the first to introduce it to Corwen seems to have been an Evan Peake (b.1758 Llandrillo) who moved to Corwen. Again, there's no immediate obvious link here.
Another likely relative is the John Moses Jones, b.1804 Corwen, to Richard and Mary who later moved to Corwen. I can't match him up either. Then there's Thomas shoemaker b.1802 Corwen, later living in Chester.
I think with regard to Thomas that 1776 baptism to Thomas and Margaret of Aberalwen, Corwen (erroneously transcribed as Llandrillo 1775 on FindMyPast) seems the most likely record as virtually all other possibilities seem to have been eliminated now, except of course for John & Hannah's child, who could well be the baptism in Chester unless there's anything else? - I was wondering if Hannah could be in the parish registers of Ruthin or elsewhere as just Ann? I've checked Corwen but with no luck.
If I can find anything relating the above people to Thomas b.1776 to Thomas and Margaret it would seem conclusive. In relation to this the only burial I haven't crossed out for Thomas/Margaret is one in 1793 (Corwen) for Thomas Jones Labourer, in Tre'r ddol, Corwen. In 1794 there's the burial for Margaret Jones, wife of Thomas (Labourer) of Tre'r ddol, Corwen. Tre'r ddol isn't the township in which they lived and there is at least one Thomas & Margaret who lived in Corwen and had children a decade before them, so this one doesn't seem likely but the only one left in Corwen. I think this must be them so they died when Thomas was 17, prompting him to join the Cheshire Fencibles, perhaps, or else they moved to Chester/Ruthin where they were buried.