[douglas]

Sorry, but just changing the direction you're ship is pointing won't change the measurements at all. You'd have to change your velocity for that, and you'd have to already know your velocity relative to the pulsar in order to tell when you had exactly reversed it, which renders the whole exercise pointless.

There's also another slight problem here. You know all these "stationary" observers we've been talking about? Technically whether something is stationary or not depends entirely on your frame of reference. There is no "absolute" or "superior" reference frame which defines what it means to be "stationary". The term "stationary" only really has meaning when you specify something like "stationary relative to the pulsar," which just means it's velocity is exactly the same as the pulsar's.