Can I (ab)use a transistor as an ESD protection diode?
Yes, there is no problem. Just connect collector to base and use that as the diode. No abuse involved. A diode, even an LL4148, is a bit more rugged than a diode-connected transistor but that should not be an issue here. 

Here is the slight overshoot in the response with the LED open and a 2N3904 connected as I suggested (+/-10V input through a 220R resistor), 10ns rise and fall times simulated in LTSpice with 1ns maximum step size: