I approach these sort of problems by having a "theory of the case". It may be incorrect, and as more information comes in I can change or abandon the current theory for another one.
In this particular case, my own present best guess (theory) is that Matilda was illegitimate, and the varying father's names and occupations reflects her way of dealing with that. When asked who your father was, or what was his occupation, are you going to say I don't know? In that situation, many just gave names. Again, this guess of mine may be completely wrong.
So, I would say OP should turn to DNA testing, and look for matches.
