The starter on almost all cars pulls the battery voltage down low enough that a reboot will happen when you start the car.
The best solution so far is a remote starter.
As long as the voltage doesn't drop below 10 volts, the AVIC should stay alive, but in most cases the accessory wire shuts down during the crank cycle since it isn't required, like the ignition wire.
A remote starter is a good option, as long as it also powers up the radio accesory wire, but it would have to be programmed as ignition, so it also doesn't shut down during the crank cycle. Also not all remote starters power up the radio accesory, and just power up the heater fan, so a relay for the 2nd accessory wire will be necessary, but again, programmed as ignition.
Some remote starters, or alarms have an auxillary output that can be triggered by remote. If that output can be programmed as a latched output, you could easily trigger the red wire to turn on before you got to your car...but it may still shut down during the crank cycle.