The phase synchronization of two semiconductor DFB lasers submitted to both frequency-shifted cross-injection and self-feedback is investigated, both numerically and experimentally. A dedicated setup based on monolithic DFB lasers permits to effectively lock the frequency difference of the two lasers on an external reference over a broad range of parameters. In agreement with a delayed rate equation model, it is shown that the sensitivity of the locking to the optical feedback phases is mitigated by using strong cross-injection thus paving the way to applications for microwave photonics. Other synchronization dynamics can also be observed, such as bounded-phase oscillations.