So I've been thinking about the variation in dice pools you (and others) have mentioned.
Tightening the range appears to be the priority here. One way to accomplish this is to limit the stacking of skills. This would also have the effect of making characters take a wider range of skills.
So here's what's on my mind: characters can only take a skill once per tier (a tier is an advancement thing that comes in later, but not relevant to starting characters). This means that they'll only get +1d6 to rolls (plus equipment and positional benefits). That will have the effect of reducing the overall range of dice pools quite a lot, likely from 2d6-4d6 on the attribute with +1d6 for skill. That's much narrower than the existing range of 2d6 to about 7d6.
The implication of that is natural talent is a much larger driver of ability than training. The variation of trained vs. unskilled becomes minimal.