I wouldn't be so chuffed about driving around with my glove box open all the time to be honest.. Maybe you should try finding an infra-red extender to place near the factory headunit so you can use the remote without having the point it at the open glove box...
I did this for my mediagate, which I keep in the middle console. The MG had an IR input though so it was simply plug and play, you're gonna need to check your headunit for one if you're into this idea.
An IR extender looks like this:
This flexible system lets you control audio/video components that are tucked away inside a cabinet or hidden in a closet. If your A/V gear is housed in a cabinet that's too shallow to accommodate the receiver, you can use this compact IR blaster to send signals to those components.
Beware of different plug sizes though.