Perusing the many old carrier pictures at Dick Copello’s Flickr pages, certain ones stand out, like these, where the loads match the carrier truck. Here’s some ’55 Studebakers heading out. Admittedly, the carrier truck does not have special two-tone paint.
1954 Fords on a…looks like a ’53 Big Job Ford. Close enough.
These all appear to be ’53 GMCs.
There’s a bit of a mismatch on the years here, but how often did one see Dodge trucks carrying Dodge trucks of the almost-same vintage?
And going back a bit further, here’s a ’34 Chevy hauling a load of ’34 Chevys, back at a time when the actual physical similarities of the bodies between trucks and cars were still very great.