The distribution of entanglement via satellite links will drastically extend the reach of quantum networks. Highly efficient entangled photon sources are an essential requirement towards overcoming high channel loss and achieving practical transmission rates in long-distance satellite downlinks. Here we report on an ultrabright entangled photon source that is optimized for long-distance free-space transmission. It operates in a wavelength range that is efficiently detected with space-ready single photon avalanche diodes (Si-SPADs), and readily provides pair emission rates that exceed the detector bandwidth (i.e., the temporal resolution). To overcome this limitation, we demultiplex the photon flux into wavelength channels that can be handled by current single photon detector technology. This is achieved efficiently by using the spectral correlations due to hyper-entanglement in polarization and frequency as an auxiliary resource. Combined with recent demonstrations of space-proof source prototypes, these results pave the way to a broadband long-distance entanglement distribution network based on satellites.