I never found the ships list but 2 guys I contacted, one a Beadling connection and the other my Gt. Grandmother Rachel's brothers descendants found this for me.
Jane was born before they married and Mary just after, so that's the date confusion. Mary was born 5 November 1834 in Houghton-le-Spring.
Mary Harrison was a witness to Rachel's marriage to George Henry Christman in Illinois.Rachel and George also names one of their son's Ralph Harrison Christman, so the name certainly is shown in the family.
I subscribe to a site here in England called "Durham on-line, that covers births, deaths etc plus censuses, mainly for County Durham but also covers Northumberland County next door.
I will look in my records that I already bought and will send Mary's birth and marriage details.If you have a email address it might be better to share info that way.
I look forward to hearing from you again, bye now and take care, Elizabeth.