I sort of finished the tablet install in the car last night ...
Physically, it worked out well. The tablet fits the existing stereo opening almost exactly. I still need to black out the area behind the tablet, and I may make a front fascia for it to blend in better with the rest of the trim.
The tablet is held in place with strong magnets on the front face of the amplifier enclosure (which I designed and built specifically so that the tablet would end up at the proper depth relative to the dash bezel).
However, I ran into a few snags. First of all, there's a lot of noise coming out of the amplifier if the tablet is connected to the car's electrical system at the same time that it's audio output is connected to the amplifier. I've ordered an audio ground loop isolator to fix that problem.
The second problem is that the amplifier itself is picking up a lot of noise, such as the heating fan motor, and perhaps some ignition noise. The amplifier is completely unshielded, and gets its ground only through the stereo wiring harness. I need to enclose it in metal, and ground it more thoroughly.