speed of light transportation would require an infinite source of fuel.
No, not infinite, just LARGE amounts of energy. All you have to do is create a bubble around you that distorts space-time; The space-time in front of you compresses you, pulling you in, while the space-time behind you expands, pushing you in. This results in movement that is fasted that light, but does not break any law of physics/relativity.
The only thing we must innovate in is finding expanded fuel sources.