My sub-field has been haunted by the fact that for slightly over fifty years the key foundation of everything we do has been in empirical dispute. The empirical anomalies have generated tens of thousands of articles. There are over 3800 for just one anomaly alone.
The problem came about because the key work was done before the mathematics had been settled and so assumptions replaced theorems. I know this because the original core set of papers have a math mistake in it. Mathematicians ultimately did learn how to solve this class of problems, but the two fields never realized that the other didn't know what the other didn't know. I found the mistake. It is subtle, but catastrophic.
I had assumed that writing a paper and doing a population test on the data we have would bring about change. Turns out that was very naive. Other than continuously presenting at conferences, what else can I do to move my field away from a technique that can be proven to be completely uncorrelated with nature? How do you get people to stop using the accepted practice? It isn't a secret that it doesn't work, but it has always been assumed to be close in some very loose sense of "close." Or rather, for a long time it has been assumed to be a poor approximation and that if the one thing causing the phenomenon were found, it would be added to the existing model and all would be great. How do you move academics when it is in the undergraduate textbooks, it is being accepted for publication, and there are seminars every year on either a new anomaly or some other factor in how it does not work?
Any strategy would be welcomed.