so the spining of the earth would propel your cargo up/down the elevator into orbit?

One thing is that west, east, north, soyth up and down are really on relevant on earth. As soon as you are talking about space everything is up(or down) but in relaity regardless of which whay yo go to get there you are fighting against gravity. I assuem this would be the reason your idea would not work but i may be wrong.