A very interesting and logical paradox for sure... but the true Ship of Theseus, no matter how many parts and pieces you may replace, are the friends we made a long the way.
In all seriousness, personally, I believe that it remains the same thing even if it happens to be changed over time with new components replacing the old ones. I feel that this paradox misses one things: the heart and soul of said object. I feel like if something still has the original's heart and soul, no matter what the physical changes on the outside and the constant replacing of old pieces, the "ship" remains due to it's core self being there. It may be a changed object (or person), but the heart and soul is there... it remains... therefore, at the end, the ship remains the same, just slightly altered.