You say:
By setting γ to 1, we obtain the result in Galilean Relativity (ie: "The time between the lightning strikes is $\tfrac{vd}{c^2}$"), which is the theory of space time before Einstein came out with Special Relativity.
But remember that $\gamma$ is not some independant parameter. It's just shorthand for:
$$ \gamma = \frac{1}{\sqrt{1 - \tfrac{v^2}{c^2}}} $$
So you can't just set $\gamma = 1$ without changing either $v$ or $c$ or both.
If you set $v = 0$ then $t = t' = 0$. In this case the events are simultaneous in both frames, but that's not surprising because if $v = 0$ both frames are the same inertial frame.
If you want to use the Galilean limit but keep $v$ non-zero the way to do this is to increase the speed of light to infinity (obviously this is a thought experiment). In that case $\gamma\tfrac{vd}{c^2} = 0$ and again $t = t' = 0$ so the lightning strikes are simultaneous in both frames.
My question is (1) how Maxwell's equations contradicted Galilean
principle of relativity.
Maxwell's equations have wave solutions that propagate with speed $c = \frac{1}{\sqrt{\mu_0\epsilon_0}}$.
Since velocity is relative (speed c with respect to what?), it was initially thought that the what is an luminiferous aether in which electromagnetic waves propagated and which singled out a family of coordinate systems at rest with respect to the aether.
If so, then light should obey the Galilean velocity addition law. That is, a lab with a non-zero speed relative to the luminiferous aether should find a directionally dependent speed of light.
However, the Michelson–Morley experiment (original and follow-ups) failed to detect such a directional dependence. Some implications are
(1) there is no aether and electromagnetic waves propagate at an invariant speed. This conflicts with Galilean relativity for which two observers in relative uniform motion will measure different speeds for the same electromagnetic wave. This path leads to special relativity theory.
(2) there is an aether but it is undetectable. This path leads to Lorentz aether theory.
Best Answer
Poincaré was confused on several points. (See the discussion on Wikipedia regarding "mass energy equivalence".) He could never get the mechanical relations straight, since he could not figure out that $E=mc^2$. Einstein followed Poincaré closely in 1905, he was aware of Poincaré's work, but he derived the theory simply as a geometric symmetry, and made a complete system.
Einstein did share the credit with Lorentz and Poincaré for special relativity for a while, probably one reason his Nobel prize did not mention relativity. Pauli in the Encyclopædia Britannica article famously credits Einstein alone for formulating the relativity principle, as did Lorentz. Poincaré was less accomodating. He would say "Einstein just assumed that which we were all trying to prove" (namely the principle of relativity). (I could not find a reference for this, and I might be misquoting. It is important, because it shows whether Poincaré was still trying to get relativity from Maxwell's equations, rather than making a new postulate—I don't know.)
Special relativity was ripe for discovery in 1905, and Einstein wasn't the only one who could have done it, although he did do it best, and only he got the $E=mc^2$ without which nothing makes sense. Poincaré and Lorentz deserve at least 50% of the credit (as Einstein himself accepted), and Poincaré has most of the modern theory, so Einstein's sole completely original contribution is $E=mc^2$.