We propose a reduced-complexity space-demultiplexing algorithm based on higher-order Poincaré spheres (HoPs) which is modulation format agnostic, free of training sequences and robust to the local oscillator phase fluctuations and frequency offsets. The signal tributaries are space-demultiplexed by calculating and realigning the best fit plane in the HoPs, with the inverse channel matrix being iteratively constructed by sequentially space-demultiplexing all pairs of tributaries. When compared with the previous proposed HoPs-based space-demultiplexing algorithm, results show a complexity reduction gain of 99% along with an improvement of 97% in terms of convergence speed.