I read about the emergency button on the stick somewhere, maybe Aviation Week, not Mad magazine, and did not make it up. Perhaps was on the later models. Would not be too hard to implement, you already have an IMU and autopilot.
It seems the fleet is in storage somewhere, waiting for the next war. Always thought it was funny that it has an F designation, for FIGHTER, but it really is a bomber. Maybe put a laser blaster on it to straighten that out.
Jet has a triple redundant digital flight control system to counter the significant inherent instability. What would this button even do? Really, really, really honest and for good stabilize it? No point. 'Bandits' I know complimented the jet's flying qualities when not low and slow. In many years of working the jet, never saw a dangerous 'uncommanded flight' problem, not once. I know the last fielded iteration of the jet, and there's no magic button. Or lasers. Or sharks with lasers. Not sure what your "IMU" reference is for, but the later jets had a very accurate, Honeywell laser ring gyro "INS" for navigation. It did not interface with the flight control system for Uber stability or anything else. The jet was known for being an unequaled bomb dropper, and the high stability was one reason why.
Also, early on, one F-117 launched an AIM-9 to be called a fighter. So, that's why it has the F designator. Probably has something to do with international treaties and such. I never saw an AA missile on a F-117A. To irritate a F-117A pilot, refer to the jet as the B-117A. Or the Stinkbug, as it sort of looks like from the back.
Not much of a secret where the jet is at today. Do some Google searching and you'll find the place. Amazing that even after all of these years and advances, the USAF felt the jet was still classified enough to warrant that kind of security. Must say something about how good the jet is, being the last, dedicated Low Observable platform built. Everything else after it was an LO design compromise, but operates on the same principals. I work on the F-35 now, but the LO How To is largely the same.
I come from a small group of USAF Airmen that don't have much if any idle speculation about what the aircraft is or is not. After a pilot flies the jet for the first time, they get their 'Bandit number" on a 30-06 nickel plated round, which is a sequential accounting of everyone who flew the jet. It's not a big number; last Bandit # ever given out went to our current Chief of Staff, General Goldfein. I am (I think) the only non-pilot Bandit, with a 30-06 bullet laser etched with "Bandit SMO", which stands for Squadron Maintenance Officer. Me and another guy who is long retired hand-picked every Nighthawk that flew over Iraq in 2003, and designed the prep plan to ensure the jets were as good for combat as we could make them before they went into harm's way. Unlike Kosovo, not a scratch, baby. Not a damned one.