I think there are two problems with the idea of trying to fit a partial charge to the SAPT electrostatic+induction curve. First, the SAPT developers have indicated that the accuracy of the SAPT components is likely lower than the total interaction energy (see this post and this post). This is because the accuracy of SAPT relies on error calcellation between the various terms in the SAPT decomposition, and this is especially true for SAPT0.
Second, I don’t agree with the stackexchange answer you linked that the SAPT induction energy should be associated with the Coulomb potential. It’s not clear how to map the SAPT energies onto the nonbonded terms in a MM potential (i.e. Lennard-Jones plus Coulomb). The four groupings of energies reported at the end of a SAPT calculation (i.e. electrostatics, exchange, induction, and dispersion) are each composed of multiple terms, and the choice of how to assign these terms to the 4 groupings is not unique. For example, Psi4 reports the exchange-induction terms in the induction grouping and the exchange-dispersion terms in the dispersion grouping, but you could make an argument that it’s more appropriate to include these terms in the exchange grouping.
For these reasons, my recommendation is to fit all of the terms in the MM potential to the total SAPT interaction energy. The stackexchange answer that you linked clearly demonstrated that fitting only the Lennard-Jones term to the total SAPT energy gives a poor quality fit, but I think that fitting Lennard-Jones and Coulomb simultaneously to the total SAPT energy will be more accurate and more chemically rigorous than trying to fit only the Coulomb potential to the sum of the SAPT electrostatic and induction energies.
As a further complication, no matter what you decide to use as your fitting target, you may have a hard time getting accurate fit parameters if you’ve only varied the distance between the carbon atoms. You should also include some conformations that have the same carbon-carbon distance but different relative orientations between the methane groups. This will allow the fit to know which variations in energy come from the carbon-carbon interaction versus the other pairwise interactions between the molecules (i.e. carbon-hydrogen and hydrogen-hydrogen).