A good replacement of the northern tool diff (since it's no longer available) is any rear axle/diff of a riding mower that has the transmission as a separate unit from the differential - simplicity, older murray's, club cadet, boden, etc. You see them on ebay often enough that you should be able to find one.
Mike's right about the two independent brake thing - it's typically to allow the kart driver to lock a wheel that's freely spinning on sand, dirt, mud to send traction to the wheel that's able to move the kart. The idea of it is pretty neat however most of the differential's that I've seen sized appropriately for karts and riding mowers are missing a few parts as compared to a full-size car - the housing rotates with the sprocket so this braking to send power to the other side only works if you're braking the wheel on the opposite side of the sprocket.
If you want a true "limited slip" with an axle like this, the solution is to have the engine drive the jackshaft fully at a 1:1 ratio and put two clutches on the jackshaft - driving a sprocket on each side of the differential but mounted on the axle halves.
