Modern LEDs may be "better", but back in the old days, LEDs were no characterized for reverse operation and were pretty poor rectifiers (I forget whether it was leakage or low and unpredictable breakdown voltage, or both). I would keep the series Si diodes. There was a lot of discussion about multiplexng back in the early days of LED 7-segemnt displays. In those days, pulsing was preferred since the efficiency went up with the instantaneous drive current so I think I is OK to run the LEDs on unfiltered pulsing dc.
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