It's been a few months, and it's time for some updates!
There were two sources of electrical noise in the amplifier mentioned in my previous post. One was differering ground levels between the tablet and the rest of the car, caused by the switching power supply that was powering the tablet. I got around this using a very simple ground isolator (basically a pair of transformers), purchased from Amazon:
https://www.amazon.ca/gp/product/B01M1671I0
That got rid of the noise coming from the tablet itself, but had no effect on the noise coming from the ignition, HVAC blower, and fuel pump. To deal with that, I installed a home made BHF (Big Honking Filter), consisting of an inductor and capacitor, as described here:
San Antonio Hams
There's still a tiny amount of crackle when the HVAC fan is on low, and also a barely perceptible fuel pump whine. I'll fix these later by adding capacitors to each motor, but it's inaudible over the road and engine noise now.