I, too, am finding this problem very difficult to solve.
But I do have a couple of problem points I need to query.
If your Thomas Bassett was born about 1720 then he would have been about 45 when he married Elizabeth Freeman in 1765.
His first child, Elizabeth, is baptised in 1766 followed by Martha in 1767 and Mary in 1769.
This seems to suggest that a baptism reasonably soon after the birth was the norm in this family.
But then we have a four-year gap until Ann is baptised in 1774.
This is not really a huge problem and it may be a case where the baptism was delayed for some reason.
BUT - the next known child, Catherine, was not baptised until near the end of 1785, a gap of almost 12 years.
Were there other children born/baptised elsewhere (perhaps Wales)
?
OR - is it possible there was yet another Thomas Bassett involved who also had a wife named Elizabeth.
Remember that IF this was the Thomas born about 1720 he is going to be about 65 when Catherine was baptised.
(Possible but .....)
I note that there is supposed to be a daughter Jane (baptism unknown) in the mix here.
AHA - I now see a little bit of light here.
Reading further notes (and now understanding them a little better) it would seem that, maybe, children of two families have been listed together and that made it appear it was all the same family.
Elizabeth, Martha, Mary and Ann were all children of Thomas Basset and Elizabeth nee Freeman.
Your CATHERINE was daughter of Thomas Basset and Elizabeth nee Glanville. - this clarifies things a little bit.
And now I might be able to throw a few more things into the mix for you to think about.
(I presume the reference to Thomas Basset "born c. 1759" is taken from IGI
- as it seems common practice in that document to place the groom's birth about 25 years prior to his marriage given a baptism cannot (or has not) been found)
Given that the earlier Thomas Bassett was married in 1765 and had children baptised in 1766, 1767 and 1769 it is NOT POSSIBLE that it would be his son Thomas who married Elizabeth Glanville in 1783.
UNLESS Thomas had been previously married.
Based on the 'supposed' birth of about 1720 and the fact Thomas married Elizabeth Freeman in 1765 (aged 45) it is quite likely he may have previously been married and, therefore, been the father of 'your' Thomas who married Elizabeth Glanville.
(The alternative, of course, is that 'your' Thomas was the son of someone else.
)
The next point may also require some careful consideration.
Thomas married Elizabeth Glanville in 1783 and, by your notes, his first two children were Thomas (1783-1784) and CATHERINE (1785-).
As Elizabeth was not the name of his first daughter I would suggest the 'possibility' that CATHERINE may be a clue and that it may well have been the name of Thomas' own mother.
The next point of serious consideration here is that, following the baptism of Catherine in 1785, it is a further 12 years before Robert appears in 1797 with further children appearing up until Thomas in 1810.
This is certainly suggestive of yet another Thomas being involved.
The fact that you have death dates for many of these children suggests that you have also recorded their AGE AT DEATH which means that we are probably not dealing with late baptisms.
So, if all the children attributed to Thomas and Elizabeth from 1783-1810 did actually belong to them - we are looking at a spread of 27 years.
I also think the names Robert, Edward and George may be significant but perhaps the most significant name amongst these later children is that of NANCY THOMAS BASSETT in 1808.
There seem to be quite a number of clues here but we need to find the information that might supply the answers.
Any further information that you may have would be appreciated and might be useful to me in trying to piece this puzzle together.
e.g. - when and where did Thomas and Elizabeth die and how old were they??
Anything at all that you might be able to add could prove useful.
If you are unsure of anything, Julia, then just send me a PM and I will take a look.