You just need a better theory that can overcome the preponderance of evidence supporting the settled theory. Something that FE'ers keep trying, and failing, to do.
Would you say that it is unreasonable of them to do so?
Why should it be unreasonable to come up with a better theory? Newton had a better theory about gravity than the settled science of the time and then Einstein came up with an even better theory about gravity than the settled science of Newton. Better theories than the settled science is how we progress. I just don't see that FE is better than the current settled science, but that doesn't mean that they should stop trying. They just need to do better. Much, much better.
So you're saying if the supposed goal is to improve something, anything you do is reasonable? Correct so far?
No, just because you have a goal of improving something, that doesn't mean that anything you do is reasonable.
The point that you appear to be overlooking is that in science there is never a simple case of "proof beyond a reasonable doubt". Instead, theories are accepted based upon the available evidence.
In some cases we know they are wrong, yet they are still used as useful approximations.
In other cases, we don't know if they are right or wrong, but they work with everything we have tested them on.
And in the latter case, sometimes we then later get new evidence to test them in and find they don't work.
And sometimes we know of situations to test in which might break the theory, but don't have a way to test it.