You may get faster random access, but with the adjusting you want to do to the other nodes, how is the overall process going to be faster?
1)...except mine will actually collapse the index when you delete an element.
2)When you insert a node, simply insert it at the proper location. Then you go back to each node in the tree, and add +1 to the number of elements.
3) When you remove a node, you basically do the same, except subtract -1 to the number of elements in each node.
In the end, you get something dynamic like a stack, but with a much faster random access rate.