Quantum states of light with many entangled photons are key resources for photonic quantum computing and quantum communication. In this work, we exploit a highly resource-efficient generation scheme based on a linear optical circuit embedding a fibered delay loop acting as a quantum memory. The single photons are generated with a bright single-photon source based on a semiconductor quantum dot, allowing to perform the entangling scheme up to 6 photons. We demonstrate $2$, $3$, $4$ and $6$-photon entanglement generation at respective rates of $6$kHz, $120$Hz, $2.2$Hz, and $2$mHz, corresponding to an average scaling ratio of $46$. We introduce a method for real-time control of entanglement generation based on partially post-selected measurements. The visibility of such measurements carries faithful information to monitor the entanglement process, an important feature for the practical implementation of photonic measurement-based quantum computation.