PNP transistor switching and inductive load
After experimenting with placing a couple of capacitors at different points in the circuit, the solution I found working best is placing a 47uF ceramic capacitor between Q2E and Q2B AND a capacitor in parallel with the LED (47uF, electrolytic). It could work with smaller capacitances, but the next smallest I have is 0.1 uF, which is not enough to completely suppress the flickering.