If you can't get your technique for upper body to work, the preferred method of takedown is to attack the knees.
Oops, not aikido.
Thinking in terms of always being vertical is quite limiting. You must observe where attacks are coming from and what areas are open to your attacks,or at least weak to defend. If you read any of Don Draeger early books about self defense, and description of martial arts, you will see how openings are attacked and defended. Even if the opponent has strong areas, be it a flurry of punches or whatever, there is still an area of weakness somewhere else.
Nice graphic Alex, but usually a hip throw is used, and you have to accept a few hits from punches, but then that is small in exchange for what you do to the puncher who becomes the winner of the slammy award.