Looking back at the gravestone evidence round about post 59 and working back I've come up with the following.
We know that Robert Swan married Isabel Hindmarsh from the marriage licence etc and that his age was 30 in 1802. Various years of birth appear for Robert according to whose research you look at but I think in the light of his own declaration in 1802 the date of baptism of 7/5/1773 is likely to be accurate.
His parents we know(from the gravestone evidence) are Joseph Swan and Ann ?
Joseph was 82 in 1826(from the gravestone evidence) making his year of birth 1744. A Joseph Swan was born in Horton, Blyth on 14th June 1744 with parents Robert Swan and Lydia or Lidia. He is the only credible option for the Joseph Swan we are looking for. Joseph Swan subsequently married Ann Hindmarsh on 22/5/1766 and so we begin to see that the Swans and the Hindmarsh's were intermarried over several generations.That may help to explain the tangle of Roberts, Isabels, Isabellas etc.
Going back further, as mentioned previously, Joseph(1744) had parents Robert Swan and Lidia/Lydia.
A Robert Swan married a Lidia Turpin on 9/7/1741 and I believe them to be Joseph Swans parents.
This appears to be the introduction of the forename Lydia into the tree and it reappears later as Lydia Swan in a granddaughter and in Lydia Gledson. I know that others have a Gledson connection to Swans.
Happy to have comments. Can anyone else add to this?