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Ford never made a dually pickup until 1980, so a 1978 IS a cab/chassis.
You will need a dually rear end with 3" wide rear leafs, the narrow leafs are always cab/chassis dual wheels. Another way to tell is the rear fuel tank, if it looks flat/wide like your F100 , the rear will fit.
Lots of people put adapters onto 3/4 ton rear ends to fit dual wheels on the back, that would be fine for you ONLY if you aren't going to haul anything in the back.
Yeah I have a posi dually and springs from a '70's rescue wagon in my '79 F250 Supercab. I only had to move the spring perches and reweld. Took about an hour with grinder and MIG. Rides a little rough empty but works really great towing and the tires last a long time.