Not Quite Star Trek

A Man rides an experimental space ship engine that pushes him close to the speed of light, knowing he'll miss out on two hundred years before he returns to normal time. Turns out they invented warp drive like a week later, but he had become too valuable as a tourist attraction to pull him out of near light speed travel, so they just... didn't stop him until the ship stopped itself. He finds the future he arrives in not at all to his liking, so he goes for another round... and another... and another. Will he ever find the star trek future he's looking for? Or will he just meet strange new alien races, and try to bang them.