The short range of outcomes can be limiting in terms of differentiating between character abilities, e.g. anything more than a +3 bonus is almost a guarantee of non-failure. If you're really keen on extending the range, try upping the dice size first, replacing the d6s with d12s for example: that gives you a lot more room in which to play around with the results and have larger bonuses as you describe.
The downside is that it drastically waters down character competence: a +1 bonus is only @25% as significant if you're rolling 2d12 instead of 2d6, so stat increments are less of a reward than new moves.
The alternative to extending the range of outcomes is to give the characters tactical options to change one type of success into another, e.g. if they accept a lesser result in advance, then any miss becomes a 7-9 instead. I think one of the hacks uses this option to add skills to the system, so that when you are using a skill, you never miss, you just get a 7-9 result instead. If that seems too effective, then a skill could extend the mid-range when used, making it 6-9, 5-9, 6-10 or whatever.