It is difficult to do anything with ordinary family name and uncertainty/inconsistency wth given names.
"....living in Mt. Moriac in 1851 and still there in 1860 "
What is your reference for them being in Mt Moriac in 1851 and 1860, and with what names...James or John, Julia or Judy?
How old are they and do you have names for their parents or children please?