I think you are far to focused on the "Swinging Ship" aspect of all of this.
The far easier way to do this, although it might be a flow nightmare would to simply build a suspended rollercoater, but have the cars seated so that it looks like a swinging coaster, the coaster could then initially travel on on a U-shaped track using linear induction motor to move it back and forth in gradually larger and larger motions mimic the movements of a swinging ship, then at one point when it would reach the peak of one side it would be boosted down toward the other side, but go past the u-shaped segment of track and continue down a series of dips and turns, then it would reach and actually peak then follow go back through the station platform area, then go past the faux peak on the other side and do a nother series of dips and turns before hitting the second actual peak and then coming back into the station and the ride would be over.
THis would more than likely have to be indoors but it could be done to look like the outside and the exterior could have like a building that appears to be blocking a real swing ship ride, like you go through the ride to get to the building, but the ship you see from the outside would be a real ship, but just for show, as when you go into the building in the que you drop below the ride and into a show building behind where the real ride would take place, the intro of the show building could be a replica of the outside area and the track could be somewhat concealed in the ceiling with a faux sky set up.
This would be the only way to do what you are proposing, with out major mechanical risks or headaches.
Below is a quick sketch showing some of the important poitns
What's the story line anyway?
