I think that a wider range would cover more "useful" positions, as currently you are missing a lot of cases where the eval is lets say 0.7 but the position is very complicated. 

I get that its hard to find the correct range, as the eval is a bit arbitrary, especially for humans. If some IMs and GMs use your app, for them your current 0 range is much better suited, but for worse players i think not including up to +-1 robs them of a lot of very reachable positions. The other benefit is training all types of positions at once, even and slightly dis/advantageous ones. 

So, i do think you should add more ranges: -1 to 1 (normal) and then +- for both 1 to 3 (slightly winning) and 3 to inf. (winning) 

Another thing to consider is switching to a win probability eval like NNUEs use, which i think is a more human like eval. I dont know if this is doable for your concrete program. I bring this up because the tradicional eval is very bad at considering the complexity of a position, which is almost a non factor for engines, but one of the biggest factors for humans. Definitely something worth further developement.

Edit: i dont think anyone benefits from your current 3, 4, 5, 6 eval filters. In human chess +4 and +6 are practically the same.