I'm wondering how fast you can strobe the LEDs before they seem continuously lit and how this compares with the persistence of the phosphor on the CRT of an analog oscilloscope. You might win 
The persistence of a LED is limited by the storage time of the minority carriers, typically in ns to the low tens of ns. GaN LEDs other than blue or UV use phosphors with a longer decay time, typically in the low 100s of ns that limits how fast they can turn off.
The decay time of CRT phosphors varies from a few ms to tens of seconds.
The turn off time of LEDs can be limited by the driving circuit turn of time as well.