What does he do when presented with more challenging material?
Faster pacing?
What would an acceleration get you that you don't have now?
Have you taken a look at the IAS?
While the not-listening-to-directions thing might be a problem in context, it isn't necessarily clear to me that (in a 5-7yo child) this is anything abnormal. It's a metacognitive skill set that is likely to be highly undeveloped in the age range, basically. Immaturity, if you will.
That's why I think you should probably be looking at tools to evaluate whether or not the child you have in front of you is a good candidate for acceleration or not.
I'd also point out that while you have teacher/tester input on your side, which is great, you may have a serious uphill battle for acceleration unless the achievement is grade-appropriate and then some. It sounds as though the achievement would support an acceleration, but that it might not produce the results you'd hope for-- in our experience, science and social studies are the areas where acceleration produces the least, and most ephemeral, improvements in fit. It also comes with costs-- increased demand on speed and executive skills. Is part-time or subject acceleration an option? Might look at that.
No helpful advice on the processing speed. Hopefully someone with more useful input will offer you some insights.
