Why vertical? Sounds harder to engineer for no obvious benefit.
Apart from that, what you describe sounds exactly like the Army cookhouse toasters I mentioned elsewhere in the thread, and which we also have in our canteen at work. A flexible steel conveyor belt[1] carries bread between two horizontal elements. You put the bread on at the front, it falls off as toast at the back and slides down a chute under the machine back to the front again. Both the element heat and the belt speed are adjustable (though you'd think only one needed to be). The only sensible way to prepare lots of toast quickly, but daft for domestic use as the heat wasted during warming up and cooling down would be out of proportion to the amount used to toast a paltry couple of slices.
Pete
[1] The belt flexes, the individual steel wires don't