This is a very interesting thought exercising , but I think I may have found "the flaw" you mentioned, specifically to do with the age of the travel.
Time is relative to gravity, so as our pilot travels the universe, time would constantly fluctuate do to traveling through a multitude of gravitation fields, all of which would have varying strengths.
Of course this is something that would be impossible to calculate until we get the entirety of the universe mapped. At least the parts the pilot would be traveling through.
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I didn't think about gravitational effects, as I set up the problem in the special relativity context. For this exercise, we may imagine those to be negligible (this strongly depends on the trajectory and we may imagine the pilot to be clever enough in setting it up).