While I know that Mr. Lee is joking, I can't help but solve the problems he posed.
Team B can fit a trailer hitch to any Honda larger than an Insight, and easily tow a 4'x8' trailer of 1000 lbs. The only larger thing I've ever needed to tow was my Insight, which, at 1800lbs, could probably have been pulled by a new Fit or HCH. Team B wins.
Team A has their work cut out for them, but again a Honda is the answer.
Truck aerodynamics are completely laughable. Team A needs a body kit to make an F150 or a Silverado shaped just like a gigantic Honda Insight (first-gen). This involves taking a sawzall to the fenders, a hammer to round out the hood, and a removable hard-shell tonneau cover that looks like a Honda hatch back. Reduce the width of the rear of the vehicle by cutting off the sidewalls of the bed and tapering them inward. There's no need for a tailgate any wider than the narrowest part of the bed, between the wheel wells. Relocate the turn signals to below the bumper to conserve precious width. The tailgate can be made of polycarbonate to conform to the Honda design language, if desired.
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The lower half of the truck's rear should be a little wider than the upper half, to accomodate a full-size rear axle. You'll need rear wheel skirts, smooth wheel covers, and no mudflaps. Underneath, the truck must be as smooth, and as tapered, as the top of the truck. Exterior mirrors can be replaced with rearview cameras, which could be mounted on an extendable boom for seeing around a trailer.
The result: With any luck, Cd around 0.28, smoother (but much larger) than most cars.
The better aerodynamics will allow you to fit a smaller, lighter engine and correspondingly smaller radiator and exhaust. If only there were more weight-reduction opportunities, people would snap up 2WD, 4cyl trucks with fuel economy gearing. Actually, I think dual-range would be a great thing in a full sized truck with a 4cyl. If a major carmaker picks up this idea, it would certainly benefit from the massive torque at 0RPM of an electric motor, which would also enable engine stop/start and regenerative braking.
There you go, truck guys. I replaced all the macho of your truck with aero and hybrid, and left you with 99% of the hauling and towing capability you had before, but about double the emm pee gees Detroit's thirstiest trucks.