Feedback for Selectable Parking Brake Bypass

Hey Guys,
I am getting ready to install a stereo system and will be taking the first step tomorrow installing a pioneer avh-p4400bh. I've read a lot about relay bypasses, warnings about overloading the remote turnon (300mA max), and functions of the radio that will not work with the bypass such as autotuning. I plan on wiring in two additional amps using the remote wire and purchased the microphone to try the autotune function. I've drawn up a circuit that I think will protect the stereo from overloading the remote as well as allowing me to switch between stock install and bypass. I am looking for your opinions and I have a couple questions to kick it off below.

1. Is it ok to tie in 3 additional grounds to stereo wire harness ground
2. If I start the car with the switch in the stock position and switch to bypass will that fool the radio that it is in park? I was told that you have to apply the brake on off on for it to work and I'm questioning whether the relay will duplicate this if it is already powered/grounded by the time I toggle the switch to bypass.

Circuit: