[Too Many Projects]

If the stars are aligned for you, the console may not need to be disturbed. There should be plastic ducts on the outlet of the heater box that can be removed for more clearance. Never done a Firebird specifically, but done plenty of others and there is usually a way to wiggle that box out or rotated enough in place to extract the core. You've worked on enough cars to recognize where that can happen once you are in it.

And L72 is right about getting yours repaired or re-cored. Most of the aftermarket stuff is ill fitting and cheaply made.