Ron, R5 and R6 need to be changed to 20 ohms for the same LED current (or V5 to 0.5V).
I did a simulation with a 10mV base-emitter offset added to Q2. The original circuit generated a current difference between the two strings of about 6mA for that. Your circuit modification had a current offset of only 0.5mA with the same voltage offset. Even a 100mV offset generated only a 5mA current offset, so your mod is like an order of magnitude better for base-emitter offset voltages (which makes sense since the degenerative emitter resister is increased from 1 ohm to 20 ohms).