Now, suppose that immediately after the electron passes through one of the slits, we make a measurement as to which slit it went through. I don't know--maybe take a picture of it (that's not really possible, but say that it is). Then in that case, the two alternative paths produce different...
I´m not a physics, so, sorry for my comentary (if it turns out to be too naive). But there is a fundamental problem, in my opinion, with your doubt. As I understand it, you presume a fixed distance (x) and the force is varying, right? Then you integrate it to get the work done (in terms of dF)...