The clocks never sync up, and neither sees the other's clock speeding up. Acceleration always slows a clock down. But when they are brought together, in the same frame of reference, the ship-board traveler and earth-bound fellow will both agree that it's the ship's clock that had slowed down.
Something about that isn't sitting right with me. Maybe I just need to chew it over (it's been many years since I tried to figure out relativity). "Acceleration" according to what viewpoint? And if the effect of any acceleration in any direction is to always see the other clock as slowing down, wouldn't that cause light from the other source to seem to be moving faster or slower than c (an effect that relativistic effects are supposed to cancel out, so that all parties always observe light from every source to be precisely c)?