I had a similar issue on my parents old Century (same year as yours btw). All you have to do is hit the eject and use something thin to push the tape up a little bit. It should eject the tape that way.Last summer that tape got wedged in there (no idea what the tape is of) and I've been unable to get it out. Pressing the eject button just causes a grinding noise of sorts and then "err" shows up.
I've heard stories about changing the gasket on an older Northstar and it's a 12+ hour job because you have to unbolt the exhaust system as well as a slew of other crap just to get to it. That isn't, or shouldn't be the case here.
You obviously do not know the history of the 3.8. Check with Pontiac GTP owners and they will tell you the same, the engine has it where it counts.
A stock Mustang GT is not really all that fast, or powerful.
Buick has been almost all FWD since the 80's. The last RWD Buick made in the US was the Roadmaster, and that wasn't much more than a Caprice with a few styling changes.