The toy model shows that if an additional charge is added in the center, that we then have a negative shift. I don’t think that the extra charge is the reason for the opposite sign. We could subtract epsilon/2 charge from the two electrons and the effect would still be negative, since the electrons are much further away.

If the formula of the monopole shift was used, we would also have a positive shift. However, I think in this definitely non-spherical case, we have to take higher order shifts into account next to the monopole term. I expect the higher order terms to be larger and giving rise to the negative shift.