The tape sounds like a natural solution. If you try to use the existing strings, you will also need to secure the other end to the soundboard – might as well use that tape. Otherwise the strings will end up in a tangled mess. I've never seen a rail on the top of a soundboard for 4' strings. All the harpsichords I have worked on, and the 2 I built, had rails glued to the underside of the soundboard and the hitchpins just went into the top of the soundboard. Sounds like an odd beast. Good luck!