Sage, so I get what we're brainstorming about, are you thinking of a normal two-wheeler that depends on centrifugal force in the wheels to balance, or something that is freestanding even at a standstill? Something that doesn't fall over at a stop is what you need on the playa, and your sidecar idea would be perfect to stabilize the thing. It would also make it more visually interesting (important for a playa-driving license) and haul more people (also important for getting a license).
If you haven't already gathered, mutant vehicle licenses are granted kinda' on a curve. The more people that will get to ride with you, the less the standard of awesomeness, the fewer people it carries, the higher the overall "wow" level is expected. So, yeah, that sidecar would be strategic in lotsa ways. And it's fun to bring company as you cruise.
If you had a fan in your barrel, I don't see why you couldn't put some wooden slats or louvers at the ends to conceal the mechanical workings. You'll definitely want your barrel to have easily removable sides for engine access, and the seams wont even show because of how barrels are made. I love the engine-in-a-barrel!
Car-type electric fans can be had ultra cheap at wrecking yards. Most are "puller" fans, mounted behind the radiator. If you want a "pusher" type, I've found that old Volvos contain great ones. Fans powerful enough to keep your motor cool draw a lot of power - you'll want a car-type alternator. That ought to be easy to drive off a belt from your motor.
Especially in recent years, another big thing to think about as you plan is impressive nighttime lighting effects. That's what the DMV expects in order to grant night-driving licenses. And - they haven't posted it anywhere yet, but on-playa there is a new reg requiring two red tail lights on all mutant vehicles. Enforcement is hit'n'miss, but just so you have the heads-up on that... make sure to hit that point. You also need a headlight, as well as the general overall cool-looking lighting.
The DMV has been known to be less than receptive to motorcycle-type vehicles, so make sure you cover all the bases to increase your odds of getting your sticker!
Too much is not enough, and when in doubt double it.