That's such a fun and creative idea, I'd love to implement a turtle with that skill as well. Unfortunately, here comes the sad part, digging upward isn't possible due to a technical limitation that's pretty deeply baked in.
To keep the game running smoothly, the cells outside your current viewport are permanently pruned (basically removed) to free up memory. Without that system, once you dig past a certain depth, around 30 or so, the game starts to lag badly, and it only gets worse from there until your browser eventually crashes. So the game is just not built to support storing information on so many cells at once. Still, I really love the idea :)