Correct me if Im wrong but the taking infinite energy thing requires mass to be part of the equation and photons have no mass. This seems to be much more related to quantum mechanics than relativity..
Usually these apparent paradoxes are resolved by using a [quantum] wave formulation of the particle - it's possible that the leading edge of the wave could get there faster than the speed of light, but to balance things out, there would necessarily have to be a trailing edge of the wave which got there slower than the speed of light.
Lately, the big question has been: Is there any way you could embed a piece of information [something like a binary "0" or "1"] in the leading edge of the wave so that that information could arrive and be understood "coherently" before the trailing edge of the wave catches up and cancels out whatever information you thought you had received in the leading edge.
That ideal is kinda the ne plus ultra these days, but no one seems to have been able to do it yet.
Photons are protestants? Mercy!
Does the Pope know this?
Photos have relativistic mass. They just do not have classical ; i.e. "rest" mass.