I've got no recommendations here, this is more by way of an observation, although more experienced ebikers than me may want to give their sixpenn'orth.
I've found that lateral, ie sideways stiffness is of great importance, if the carrier can move sideways it seems to begin to oscillate out of sync with the bike and induce weaving. Another factor is height, the higher it is the worse the wobble. Thirdly is the position of the load relative to the rear wheel spindle, if the bulk of the weight is behind the spindle then any wobble is magnified by the pendulum effect of this weight.
Obviously the steering characteristics of the bike frame and forks in the form of rake and trail have an influence, and some framesets may be better than others, but that isn't the sort of info we normally have access to.
Finally, the other feature to bear in mind is the position of the bulk of the weight of an ebike, the battery. If this is in the centre of the bikes frame, between the riders legs, good. Behind the rider, bad. There is a relationship between the mass in front of the rider and the mass behind, in terms of the forward weight damping the movement of the rearward weight.
I've found that lateral, ie sideways stiffness is of great importance, if the carrier can move sideways it seems to begin to oscillate out of sync with the bike and induce weaving. Another factor is height, the higher it is the worse the wobble. Thirdly is the position of the load relative to the rear wheel spindle, if the bulk of the weight is behind the spindle then any wobble is magnified by the pendulum effect of this weight.
Obviously the steering characteristics of the bike frame and forks in the form of rake and trail have an influence, and some framesets may be better than others, but that isn't the sort of info we normally have access to.
Finally, the other feature to bear in mind is the position of the bulk of the weight of an ebike, the battery. If this is in the centre of the bikes frame, between the riders legs, good. Behind the rider, bad. There is a relationship between the mass in front of the rider and the mass behind, in terms of the forward weight damping the movement of the rearward weight.