I generally agree with you, except for the fact that it was more of an aerodynamic issue than a center of gravity issue: the large body of the engine produced lift at higher angles of attack, making the nose go up and worsening the problem. The fact the engine was more powerful also contributed to that problem: the higher thrust produced more upwards torque.

And I am not saying that the software bandaid and the goal of avoiding a new type certification is a bad thing. In fact, it is done all the time with no ill effect.

What I am saying is that they did it wrong, and that's the real problem. Your explanation on what they did wrong is, I think, entirely correct.

My hypothesis is that if they didn't care about keeping the same type rating, they probably could have skipped the bandaid and trained pilots to just keep out of that dangerous configuration, just like pilots are trained to recognize, avoid and recover from stalls. It didn't look like an unmanageable problem for pilots, more like something they needed to be aware of and train for.