Just looking at this from a theory/fundamentals understanding, without the aid of years of experience, I would suggest that the issue has to be on the downstream side of the GFCI.
Not discounting the years experience of other members; It seems like it's irrelevent what is happening up stream because the GFCI will only trip if the ungrounded conducter and the grounded conductor do not balance.
I would suggest looking for a hidden connection of the neutral of the GFCI's circuit with a different circuit Downstream of the GFCI, or a neutral ground connection Downstream of the GFCI.
But first replace the GFCI with a new one to rule out a faulty GFCI
Or it could be that the GFCI is doing its job and there is an appliance that is faulting