Ground when armed radio on until door

Hey I installed the radio on until door opened on my car.  It works great except for the fact I have remote start on my car and when i remote start it and when i turn it off the radio and other accessories remain on.  Since I use passive arming I want to know if I can use the ground when armed output of my alarm and also the standard door  ground input to turn the radio off .  My alarm is the Viper 790xv and the ground supplied by the ground when armed wire is rated at 500ma.  Here is the radio on until door opened drawing I used to install it on the car. 

The radio on until door opened setup works perfectly...the only problem is when i remote start my car with the transmitter the radio stays on after i shut it off with the transmitter.   I want to know if there is someway that i could wire it up to make the radio shut off after i have killed the car with the transmitter after i have remote started and turned the car back off without opening and closing a door.    I would like to use the ground when armed wire to do this.

i think this is a better way to put it....i want my ground when armed wire to do the same thing as the door trigger wire (turn the radio off when the key is not in the ignition) because when i remote start my car and turn it off by my transmitter the radio stays on  and i  have to go to my car and open the door for the radio to go off.  i want to be able to turn the radio off with my transmitter(preferably automatic with the ground when armed wire off my alarm).

yes i  would like for the radio to come on during a remote start.   i would just like to be able to turn it off after i have turned off the remote start with the transmitter.  my car is a 1993 buick roadmaster.

thanks for being so patient with me...