That POP! is likely the switching of the speaker from the audio amp. The speaker amp is used as a modulator amp when you transmit. Maybe try an electrolytic capacitor on the + speaker lead. + side to radio and - side to the speaker + connection. Try anything from 10 uF to 470 uF. Value is not that critical.
Yeah the chip is on all the time but the input and output is switched from a speaker amp to a modulator amp. Something that is being switched must be causing it either audio or DC control. If I can find the time I will look at the schematic. Don't hold your breath however. I'm on my last couple days of vacation and got called back to work tomorrow for overtime. Oh yay.