I have to ask... why do you want previous/next sibling to be stored in separate columns and is it actually essential to use "Z", "A", etc for your hierarchical path? The reason I'm asking about the siblings is because I think they're unnecessary and looking for a reason why you think you need them. The reason why I'm asking about the hierarchical path is because having them lettered in such a fashion is going to be a continuous pain for you to maintain.
And, to be totally honest, that -1 thing is a huge pain when it comes to properly constraining this Adjacency List. It's one of the places where a NULL would be much better suited.
IF we can do away with the prev/next sibling columns and the funcky lettering in the hierarchical path, then I can show you some things that might just make your day.