Experiments demonstrate that under large epitaxial strain a coexisting striped phase emerges in BiFeO3 thin films, which comprises a tetragonal-like (T') and an intermediate S' polymorph. It exhibits a relatively large piezoelectric response when switching between the coexisting phase and a uniform T' phase. This strain-induced phase transformation is investigated through a synergistic combination of first-principles theory and experiments. The results show that the S' phase is energetically very close to the T' phase, but is structurally similar to the bulk rhombohedral (R) phase. By fully characterizing the intermediate S' polymorph, it is demonstrated that the flat energy landscape resulting in the absence of an energy barrier between the T' and S' phases fosters the above-mentioned reversible phase transformation. This ability to readily transform between the S' and T' polymorphs, which have very different octahedral rotation patterns and c/a ratios, is crucial to the enhanced piezoelectricity in strained BiFeO3 films. Additionally, a blueshift in the band gap when moving from R to S' to T' is observed. These results emphasize the importance of strain engineering for tuning electromechanical responses or, creating unique energy harvesting photonic structures, in oxide thin film architectures.