But didn't Einstein write the following in his own book?
“I believe in intuition and inspiration. … At times I feel certain I am right while not knowing the reason. When the eclipse of 1919 confirmed my intuition, I was not in the least surprised. In fact I would have been astonished that it turned out otherwise. Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.”
On my first reading I took "novel study path" to mean new research techniques or something along those lines, which seems obvious and is not likely what you meant.
And you still need a good amount of creativity to come up with special relativity and to a certain extent, with the photoelectric effect (though we could say that was the 'easy' one)
But yes, the puzzling results and existing mathematics were part of it. But there is a reason we hear much more about Einstein than Lorenz or Michelson-Moreley
If you mean the Michelson–Morley experiment (apparent zero velocity of earth with respect to the ether), apparently Einstein himself claimed that wasn’t a motivation.
I believe it was all about resolving the long-standing "action at a distance" question raised by Newtonian physics (Newton himself noted that this was philosophically disturbing but didn’t venture an answer). Intuition and philosophy, rather than experimental evidence and mathematics.