For posterity, this issue is partially resolved when the AMP C cable from the harness is connected to the AMP CONT cable coming from the speaker output and SIM card connector cable. If you don't have an AMP C cable exposed, connecting the AMP CONT cable to the CANbus's ACC pin will work (in my case it was Pin 9).

After that, update the MCU by extracting the files from here into the root directory of a USB drive and restart the head unit. More information can be found in this post. The speakers should no longer pop when starting the car from a shutdown but will if manually rebooting (will be fixed in a future update).