I'd argue that we'd have two sister ships. You can never totally replace every part on a ship, because one of those parts is human in nature, a human fingerprint created by the identity people assign to it. It's an individual because people identify it as such. 

The first ship, the one that's been kept in service yet had every part replaced, that is constantly perceived as the same ship since it's still fulfilling it's purpose.

The second ship, the restored model, is still the ship of Theseus, because someone who served on the ship would still be able to identify the individual parts by memory of what broke and what caused them to break. All it would take is for one individual to recognize this and identify it as their old ship, reassembled. It would be trippy to see them together but I don't think that's insurmountable.

TL;DR the ship is an idea, the idea is a unique and inherent part of the ship, and if you replace every physical part of the ship you've still only replaced most, not all of the ship as the idea still remains.