Hashing using search trees instead of lists
For lists, insertion, find and delete are respectively in $O(1)$, $O(n)$, $O(n)$. Sorted list are worse. Binary search itself is for sorted arrays, in which the operations are in $O(n)$, $O(\log n)$, $O(n)$. If you want "insertion" and "delete" operations then you need more than just binary search.

You probably want something like binary search trees. It is a lot easier to find references about it once you have the proper terminology. These operations are in $O(\log n)$ worst-case time, for example for the implementations using AVL trees and red-black trees.