Let’s say the photons are like marbles in a pipe that is full from end to end. You push one marble in one end, and a marble pops out the other end. The marble didn’t travel, it just took up a place that made another marble leave its place. Einstein’s speed limit is secure...........
Bean bag.
Well, no. In order for your thought experiment to explain this result, the pressure from your finger would have to propagate through the string of intervening marbles, to the last marble, faster than light speed. And since neither marbles nor any other real substances are incompressible, I think you'd run into relativity troubles at the atomic level.
Applying your analogy to a string of photons, you're basically saying that the amplitude perturbation (which affects the wave properties of light) somehow travels faster than the photon particles.
I don't think the analogy works.