Problem with the fall time of a NPN transistor
You've probed around in a good fashion but you neglected to look at the emitter signal. It will fall more rapidly but the diode then becomes reverse biased due to stray (or actual) output capacitance holding the cathode at a positive potential therefore the true output trundles back to 0 volts much more slowly.

Between the base-emitter region shutting down and the reverse bias on the diode you have the problem. Try putting a real load on the circuit or even a 1 kohm from emitter to ground or both.