Well if the head unit and the amp have been swapped out and the problem stays you are looking at what you left behind. I know - statement of the obvious. But what does that represent?

The wiring from the head unit to the amp, and the amp to the speakers. The speakers (total of six to look at).

It might turn out that the old head unit and old amp are OK so don't pitch them yet.

Take a look at the plugs at the amp and see if any of the pinouts are bent, broken, corroded, etc. After that, it might mean going into the speakers.

The factory service manual has a section on troubleshooting the factory sound system - see if it has any symptoms described that match yours.

Another approach is to try running speaker level outputs from your new head unit (if you have them, could be RCA outputs) directly to some speakers (not the ones in the car).

That eliminates the factory amp and speakers, and the wiring harness completely. See if the same problems happen. If so, it might be a bad ground or ?? If it doesn't happen with this setup, then you're probably looking at swapping out a bad factory speaker.

It's not that likely that the harness is bad especially if you didn't cut into it.