Wow, it must have been fascinating to be that close to history!

Nope, the car still exists and is on display at the Henry Ford Museum in Dearborn (I've also been there a few times and seen it). It was always owned by Ford Motor Co., who leased it to the US Government for $1.00 a year. After the assassination, it went back to Ford, who took out the interior and stored it, totally refitted it, changed the outside to look like a newer model, and welded on a permanent steel top. It was used by Johnson and Nixon before being returned to Ford Motor.