Continued illumination of LED after removing voltage
You need to switch to LEDs without phosphors.  The original red, green and blue LEDs don't need phosphors, and should have no trouble flashing at that speed.  Some of the more modern ones use phosphors to deliver fancy colors, suck as pink.
You should be able to get reasonable illumination using a combination of red, green and blue.  You will have to tweak the currents through each LED color to get something that looks right.