I would suggest here where Einstein got his evidence. General relativity started from a simple assumption: that inertial mass and gravitational mass are the same. Before Einstein, this was a mere observation, and nobody had really asked themselves why it was so (I'm oversimplifying here of course). But Einstein stated this as a fundamental principle, an axiom if you want. And then he went on to draw what logical conclusion could be drawn out from that basic axiom. Sure it took him ten years, because it wasn't obvious at all, and the mathematical tools to do the work were relatively new and obscure. But Einstein never faltered from his initial hypothesis.
And there WAS overwhelming evidence that inertial mass and gravitational mass were the same. Nobody knew for sure if they were EXACTLY the same, but they were sufficiently similar to support Einstein's hypothesis that they were, indeed, exactly the same.
So in Einstein's mind, the fact that posing gravitational mass equal to inertial mass led, logically, to the final conclusion in terms of general relativity, plus the fact that a vast amount of evidence pointed to the two being indeed equal, all that was enough for him to have confidence in the theory. Eddington's measurement was a very difficult one, and the results far from conclusive as has been shown elsewhere. Einstein had every reason to believe that a failure by Eddington to confirm his theory would in no way falsify it (mind you, this was way before Popper and Kuhn!...).
That's my two bit of explanation here. I used to be much more familiar with the history of general relativity but that was some time ago. Maybe re-reading Pais would help confirm or refute this idea.