The filtering caps for the DDL do smooth out the waveform, I'd recommend a smaller value filter cap for higher frequencies, and even then it may be more sine than square. Since it is still constant current protected it shouldn't cause any real problems as long as the voltage is high enough, which is part of why I went for 3V extra. True TTL squarewave modulation has to be done directly to the output stage of the LM317 and not it's input power or done without filter caps and with other transient suppression. You don't want to cut the power to the diode though because it will unload the LM317 and potentially fry things.
The NPN does appear to drop voltage, but I haven't determined how much yet - 3V extra solves it though. My breadboard is fed with 8.2V, which is 3V (LM317) + 0.7V (1N4003) + ~2.75V (LD Vf) + NPN drop out (maybe 1.5V? two junctions, makes sense) + maybe a few decivolts extra. I don't have an incrimentally variable power supply so I can't test the input lasing threshhold voltage to determine the NPN dropout curve. I can't measure the NPN drop out across it like you would a passive device because my multimeter isn't fast enough to respond, I would need an oscilloscope. The 555 does not drop any voltage and only consumes a few mA.
Yes, it would probably run better with a 1k Ohm resistor between the Base of Q1 and the OUT (pin 3) of the 555, but it isn't 100% needed at low frequencies as the input impedance of the 2N222A is pretty high. You could add a small value series nonpolar capacitor as a DC blocking cap as well. You can also reverse the Collector and Emitter connections on Q1 and it wouldn't affect the performance. I left this semi-barebones for simplicity and cost. I can modify it further if needed for any particular goals.
I always put series protection diodes in my drivers for reverse protection and to help reduce over-voltage chance. I dislike parallel shunt reverse polarity protection because if the diode ever gets destroyed by overflow it will leave the rest of the circuit vulnerable. Placing it in series effectively cuts off the rest of the circuit should it fail. Sacrificial diodes FTW. Also, I tend to run my modules off 12V (or 13.8V) so they need extra voltage sinking if they aren't 450s or 405s (5V Vf + 3.7V DDL and Series Diode + NPN drop + more diode shunts/clamps if needed). I left the DDL driver seperated from the pulse circuit on purpose for this reason, it isn't a mandatory part, just a bonus for anyone who might need. This circuit should work for all drivers at low pulse rates, high pulse rates may interfere with boost/buck drivers (I don't know if it will though!).