"And you cannot assume constant 1g acceleration the whole way. As you get closer to C acceleration will get exponentially more difficult. "


Nope. To the pilot, it will be 1g at all times. Got to look at it relativistically.- His speed will approach cee, but never reach it- and time will slow down as he gets faster. in HIS ( or her) frame, it will be constant acceleration at 1 g, to an observer on Earth it will look like he is traveling just below cee ( need to have the light-cones to see the actual "apparent" velocity, as the light from the moving spacecraft will be both frequency shifted and seen at some time later ( based on distance from the observer.)