Distributing entangled states over potentially long distances provides a key resource for many protocols in quantum communication and quantum cryptography. Ideally, this should be implemented in a heralded manner. Starting with four single-photon states, we cascade two single-photon path-entangled states, coded in orthogonal polarizations, to distribute and herald polarization entanglement in a single quantum repeater link architecture. By tuning the input states to minimize (local) losses, the theoretically achievable fidelity to the target state without postselection approaches 1, while sacrificing heralding rates. We achieve a fidelity to the target state of over 95% after postselection, providing a benchmark for the experimental control and allowing a first demonstration of a device-independent quantum key distribution architecture capable of operation over relevant distances. We show that the fidelity of the heralded state without postselection scales predictably and also identify various practical challenges and error sources specific to this architecture, and model their effects on the generated state. While our experiment uses probabilistic photon-pair sources based on spontaneous parametric downconversion, many of these problems are also relevant for variants employing deterministic photon sources.