Interesting dilemma.I'm 5-foot nothing, so I can't relate. LOL!
But I don't think I've ever heard of anybody scrubbing the shelf itself of a rack. Is the rack too heavy to lay on its side?
How about using one of those bendable dusting wands - you can put a scrubbing pad instead of the dust cloths on it so you can just use it to reach under the shelves?
But really, I don't know if any of what I said above would help. Just throwing ideas out there.