We use first-principles methods to study doped strong ferroelectrics (taking BaTiO3 as a prototype). Here, we find a strong coupling between itinerant electrons and soft polar phonons in doped BaTiO3, contrary to Anderson/Blount’s weakly coupled electron mechanism for "ferroelectric-like metals”. As a consequence, across a polar-to-centrosymmetric phase transition in doped BaTiO3, the total electron-phonon coupling is increased to about 0.6 around the critical concentration, which is sufficient to induce phonon-mediated superconductivity of about 2 K. Lowering the crystal symmetry of doped BaTiO3 by imposing epitaxial strain can further increase the superconducting temperature via a sizable coupling between itinerant electrons and acoustic phonons. Our work demonstrates a viable approach to modulating electron-phonon coupling and inducing phonon-mediated superconductivity in doped strong ferroelectrics and potentially in polar metals. Our results also show that the weakly coupled electron mechanism for "ferroelectric-like metals” is not necessarily present in doped strong ferroelectrics.