Einstein in his thought experiment(?) for the constancy of speed of light in vacuum in all frames reasoned , that if speed of light of vacuum isn't constant than you'll be able to perceive effect before action .
Hm, as far as I know his reason for saying that the speed of light is constant is the following:
The speed of light in a vacuum is something that comes out mathematically from Maxwell's equations.
Einstein assumed that physics is beautiful and got rid of the privileged (aether) frame, and then took the following situation:
Alice and Bob are in identical boxes floating around in space, with Bob's box moving at $v$ relative to Alice, with no external (or cross-) influences. Both of their boxes contain world-class all-purpose physics laboratories (in technical terms: a reference frame). If the privileged frame existed, then even though all other experiments show that the boxes are subjected to the same physical conditions, any experiment made to measure the speed of light (this can be easily done by tossing a bunch of electrons around) would give different results. However, this doesn't sound quite right, since $c$ is something that pops out of Maxwell's equations--it's a fundamental constant (unlike the speed of sound, which depends on the circumstances leading to the sound). If the privileged frame held true, then Maxwell's equations would get ugly for moving frames.
Also, the "ugly" aether-versions of Maxwell's equations didn't hold up to experiments like the Michelson-Morley experiment.
Note that this does not apply for light in a medium. When light travels in a medium, Alice and Bob can detect a difference in their situations as they can measure the relative speed of the medium (which differs by $v$ from their frames).
The time dilation bit came after this postulate as far as I can tell, and depends on it. The reasoning in your first sentence("you'll be able to perceive effect before action .") can't be made unless you assume that simultaneity is frame dependent, and for that you need the framework of special relativity, and for that you need the speed of light to be constant.
Side note: In any medium, the maximum speed of any readable communication of information is $c$. Particles going faster than light in a medium exist (for example, cooling moderator rods from a nuclear power plant kept in water emit faster-than-light-in-water neutrons, which emit Cherenkov radiation (a sort of "sonic boom for light")
