Efficient 3 dimensional position or range queries (line/column/page) is a pretty well studied problem. You don't need to query every point of the space to answer anything.
It's a task more commonly found in computational geometry (3D range query == find all the points in a data set enclosed by a cube).
There are numerous data structures that are well suited for various geometric queries like ranges/lookups (interval trees, quadtrees) as well as more text-oriented operations like cut/copy/paste/insert/merge/etc (like ropes).
I'm not familiar with the operations required to put a cursor at the right place in a document, but knowing how much research has gone into storing similar data and looking up what you need efficiently the idea of "going through all the text every time" is a big code smell.
