In 1967, it would have been Seaboard Coast Line, which was the merged Seaboard Air Line and Atlantic Coast Line railroads as far north as Richmond, and then the RF&P (Richmond Fredericksburg and Patomac from there in to DC, although to be exact, the part form the south bank of the Patomac River ot Viriginia Tower would have been operated on the tracks of the Pennsylvania Railroad, and the last mile or so in, including the tunnel just east of the Capital Building would have been on the track of the Washington Terminal Company.
The exact routing south of Richmond would have depended upon which train you were on. All passenger trains north out of Ft. Lauderdale at that time would have been on the ex SAL line at least as far as Auburndale. If you happened to be on one of the formere ACL trains, such as the Champion, you would have turned rigtht there and goen up through Orlando, then Jacksonville, Savannah, Charleston, Florence, Rocky Mount, Petersburg, Richmond. If you happened to be on one of the ex SAL trains such as the Silver Meteor or Silver Star, then you would have continued north of Auburndale through Ocala, then into Jacksonville, Savannah, Columbia, Raleigh, Petersburg, Richmond.
In 1967, if on the SAL side, you may have been on the former SAL track between Jacksonville and Savannah, or the former SAL. The SAL line which was all single and closer to the coast with longer bridges was abandoned and all traffic moved to the slightly more inland ACL line, but I do not know when that occurred. Also, at some point shortly after the merger, a connection between the SAL and ACL was built on the south side of Petersburg VA and after that all trains were on the ex ACL line from that point north into Richmond. This connection was in place by the mid-70's, but not sure about 1967, as IIRC that was the year the merger occurred.
Why not go ahead and register here? The benefits are tremendous! Let's see they are . . . , well, it is nice to simply be here.