Aaron, thanks a lot for the nice pics. I have to repair a PSU, too and that will help a lot to reassemble the unit.
Concerning your crackling noises: Do you still have these noises when using the headphone jack? So you can diagnose if the crackling comes from the players electronics or from the amplifiers. Each speaker has his own amplifier as far as I know.
Is it possible that the cracking is caused by a defective connection inside one of the connectors. Maybe you should check this.
Moreover, maybe the cracking depends on the power stability. So I would check the 9.5V/19V PSU outputs with an oscilloscope or a memory digital multimeter to detect if the cracks are caused by a breaking down voltage for a moment.
Did you check your radio with a non-shielded PSU? If yes it is possible that under higher currents (louder play) the PSUs HF field distorts one or more of the internal amplifiers. I think you must shield the PSU like build in when testing.
Hope this helps. If not please write again.
Greetings from Germany.