Weird request

[Ombligo]

put a second dummy doorknob on the inside up where you want it - just on the inside, mounted to the door, just one handle nothing else. Then fit a large, tight, loop connecting both knobs (think innertube rubber band). When you turn the top handle, it should turn both via friction.

You could do the same basic concept with a sprocket in place of the main knob, then a crank handle at the height you want, connect the two with a bike chain. Turn one, and the other works.