The actual regulation may not say "bed" but may refer to an opening from the passenger area to the cargo compartment. If you made a Bronco/4Runner-like vehicle, that would be an SUV. I do recall Subaru creating the BRAT with the jump seats in the bed to make it a passenger car and not a truck, therefore evading the tariff.
The "chicken tax" only applies to countries that the US does not have trade agreements with. If you were to build a truck in countries like Chile or Israel or the Dominican Republic, your vehicle would be exempt. Australia and Thailand have been working on similar agreements (the former may already exist).