The functionalities of BiFeO3-based magnetoelectric multiferroic heterostructures rely on the controlled manipulation of their ferroelectric domains and of the corresponding net in-plane polarization, as this aspect guides the voltage-controlled magnetic switching. Chemical substitution has emerged as a key to push the energy dissipation of the BiFeO3 into the attojoule range but appears to result in a disordered domain configuration. Using non-invasive optical second-harmonic generation on heavily La-substituted BiFeO3 films, it is shown that a weak net in-plane polarization remains imprinted in the pristine films despite the apparent domain disorder. It is found that this ingrained net in-plane polarization can be trained with out-of-plane electric fields compatible with applications. Operando studies on capacitor heterostructures treated in this way show the full restoration of the domain configuration of pristine BiFeO3 along with a giant net in-plane polarization enhancement. Thus, the experiments reveal a surprising robustness of the net in-plane polarization of BiFeO3 against chemical modification, an important criterion in ongoing attempts to integrate magnetoelectric materials into energy-efficient devices.