I agree with dazeakamike. That's what I would try to do if possible. Remember, there is a bracket that holds the radio to the dash frame. The original T/A stereo's have a nut and stud on the upper, rear, drivers side of the radio that fits into the slot of the bracket and gives some support.
The brackets are really hard to find since they get tossed when an aftermarket radio is installed. The radio's you buy on ebay may look original, but it they are not from a firebird, they may not have the stud and nut on the drivers side since other GM divisions used different types of brackets.
Check the service manual and you'll see a drawing of the radio and bracket.
If you need a picture of the bracket (it's not much to see) I have one and can send you a picture of it if you send me a message.