"it was trivial to randomize the parameters within their bounds of experimental measurement and create chaotic systems. Did this mean the model wasn't so great? No, it just meant those couldn't be the real-life configuration of those parameters . . . sigh."

Why is this sigh-worthy? Maybe the model is still ok. Maybe some of the parameters are constrained in nature in ways that you/we just don't know about yet. Of course, it could be that the model is bad, but you act as if your results, as stated, demonstrate this. Which they do not, as far as I can see.