Complicated capacitor LED driver model test

I decided to do the "LED experiment:" how fast can I charge a capacitor with a silicon 2N4123 transistor current follower — something like 10 µF — and how long will it for its charge to dissipate through the LED? In other words, how many LED's can I continuously refresh using this technique? My 20 mA LED that drops 2.2 volts will need about a 340 ohm resistor. It takes about 240 µs to charge a 5 µF capacitor to nearly full voltage — about 500 µs to squeeze in the last few millivolts. Dissipation takes only 650 µs to fall a full volt.

After a few iterations, I settled on a Darlington follower which drops the charge-time to 20 µs. Given a 1 µF capacitor, the rise time is below 10 µs and the decay runs for about 215 µs. If I move up to a 5 µF capacitor, the rise time stays below 10 µs but the decay jumps to 650 µs. If I then move up to a 10µs capacitor, the decay of 1 volt loss jumps to 1.4 ms.

Comparing to the prior pulse-width modulated test, I found the duty cycle needs to be about the same for the same brightness: 28 µs of the 2.1 ms cycle time or 1.3%, so I can theoretically drive 75 LED's in a perfect world.