Due to the long electrical screening length of an insulator, changes in local ferroelectric (FE) polarization can cause significant electrostatic potential drops or rises across the whole insulating region, which can be designed to enhance the tunneling electroresistance (TER) effect. First-principles calculations of ${\mathrm{Co}}_{2}\mathrm{MnSi}/{\mathrm{BaTiO}}_{3}/{\mathrm{SrRuO}}_{3}$ multiferroic tunnel junctions predict a unique local FE polarization at the MnSi-${\mathrm{TiO}}_{2}$ interface, which is giant (tiny) in the right-polarized (left-polarized) state. For the right-polarized state, the large interfacial FE polarization greatly lowers the FE barrier height, making it close to zero. However, for the left-polarized state, because its band edges near the MnSi-${\mathrm{TiO}}_{2}$ interface are usually below the Fermi level, the tiny interfacial FE polarization has a weak effect on the electrostatic potential, maintaining a sizable barrier height. This FE-controlled barrier height produces an optimistic TER ratio of up to $1.1\ifmmode\times\else\texttimes\fi{}{10}^{3}$. Even if the large interface polarization is unexpectedly fixed, the TER ratio remains ultrahigh, increasing the fault tolerance of the interface-enhanced TER effect in applications.