I don't think that a TBT cart pulls more down a hill because there is so much weight transfered to the tractor. As well, the forward movement as well as the drag provided by the implement in the ground tends to have the setup pull straight.
Because of the fixed axle, as soon as a TBT cart would begin to slip down, the tires immediately point up the slope again, steering the cart back online. This doesn't happen on a TBH because of the caster on front.
I think the biggest problem with a TBH on a hill is the castering front wheel(s). The wheel doesn't provide any directional stability, but steers down the slope automatically, which skews the back of the drill. Perhaps if the front of the cart was hooked directly to the drill to the axle (not able to turn in relation to the drill) and had a 5th wheel style hitch on top to allow the rest of the cart and rear axle to turn it would work better. This is similar to seedhawk carrying much of their weight on the rear of the mainframe.