You can actually give a semi-plausible justification of special relativity based on what was known in 1901. Maxwell's equations are fundamentally incompatible with...
Yes, this is the chain of logic that Einstein followed in 1905. But it was followed in 1905, not 1901, despite plenty of other physicists focusing on the question.
There's a reason why I did not list the "semi-plausible justification" in my account of the Bizarre Speed Limit. People typically try to judge absurdity by surface features, without in-depth study of a topic.
Suppose I told you that I knew for a fact that the following statements were true:
You’d think I was crazy, right?
Now suppose it were the year 1901, and you had to choose between believing those statements I have just offered, and believing statements like the following:
Based on a comment of Robin Hanson’s: “I wonder if one could describe in enough detail a fictional story of an alternative reality, a reality that our ancestors could not distinguish from the truth, in order to make it very clear how surprising the truth turned out to be.”1
1Source: http://lesswrong.com/lw/j0/making_history_available/ewg.