My summary of the position is as follows:
The only evidence of the likely birth date for Jane Daniel(nee Jones of Llanfaglan,according to the baptism records of her children,nee Roberts from her marriage record)is from the 1841 census(to be treated with caution because 45 y.o/1786 may be rounded to the nearest 5),and the passage record to USA where she is given as 60 in Aug 1845,i.e born1784/5.
Records are generally of baptism rather than birth which can be any time later,but a working hypothesis for a baptism record is 1784-1786.
Because of the constraint of the cousin relationship to Foulk Roberts and the reference to her as Jane Roberts elsewhere,the favoured record sought is the birth to a John Roberts,son of Robert J E Roberts(aka Robert Jones as per his will of 1795),with patronymic naming giving the reason for the marriage record,and considerations including the nature of database transcribing ("Jane daughter of John Roberts") giving a baptism record of Jane Roberts.
The only record that appears to fulfil these criteria is that of Jane Roberts,1786 Llanfaglan daughter of John and Margaret who may be the same parents of William(1772) "son of John Robert,labourer of Ty Eiddew,and his wife Margaret"
Ty Eiddew is established as the home of Robert J E Roberts at this time by virtue of his own son William's birth there in 1767 and it being his address on his will of 1795.
However,the necessary birth date for such a John Robert(s) is in conflict with published trees.
It is unlikely that he had a second son John(1765,published trees) while the first was living.
No record for the baptism of any son John has been established,but there is a clear reference to such in the 1795 will.No record of a burial or will has been clearly established(The Ty Newydd John Roberts was a mariner)
Further, no sibling relationship has been established between William(1772) and Jane(1786),or with any other possible sibling Robert (1775) and Richard(1783).The possibility of another John and Margaret Roberts in Llanfaglan can not be discounted.
There is no continuity of abode or similar information to identify John and Margaret in these records.
Having said all that there is nothing I can see at the moment by way of a fatal flaw that prevents the 1786 record being appropriate.
Regards
Roger