I just watched the You tube video, the automatic trans is a C6 not a C4 as the C6 has no removable bell housing, no removable servo cover on drivers side and it has trans pan with square notch in the rear of it. I was a Ford Trans tech for 40 plus years. I hope this helps.
While I was going to college I used to pump gas at my brother's FINA station, he had a 56 Meteor (identical to the one pictured above), I thought it was neat the crown trim was also part of the headliner.
There were numerous body alterations being done, altered wheel base, body mods, front ends being narrowed, rain drip rails being removed etc. IIRC there was a magazine article at the time about things that were being done.