I agree with mon and dbat, I suspect that your son is having some other issues. Did your private testing include achievement tests or any suggestions for further assessments based on his largely uninterpretable IQ test? It sounds like he has some real output issues but I don't think that you have enough information to determine whether it is dysgraphia or some other expressive disorder. I would not assume that this is all "executive function" issues. Your kid is 7. It is perfectly normal for this age to have minimal organizational skills and short attention span for boring tasks. What I think you need to figure out is why he is avoiding the certain tasks. It sounds like something more than just boredom.
I agree with knute (and mon and dbat!)... and I've read your follow-up to knute. You'd really benefit (jmo) from further testing to tease out what's up with the discrepancy in processing speed - it could be fine motor, it could be vision, it could be something else. Most of us who's kids have been through neuropsychologist testing have had a few additional tests done that you don't mention - tests that give details re fine motor function (not an OT type of test, but looking at how the brain controls fine motor) and vision (again, not the type of test an eye dr would give, but tests that give clues re how vision is actually working in a setting similar to skills needed for academics). My kids also had other executive function type of tests as part of their neuropsych evals. Soooo... you've got a lot of good information so far, but there are tests out there that could possibly help you understand what's up with the IQ subtest discrepancy in more detail - and that could be very important detail.
Knowing that your ds has a history of strabismus, I wouldn't be surprised if the low processing speed is tied to a vision issue. I have an adult relative who had strabismus as a child that is well-corrected as an adult with contact lenses... but she still struggles with reading. Not in a huge way - she's been very successful in school... yet not quite as successful as she'd hoped to be or as most of her professors who know her well enough to know her intellect think she would be. I also have a dd who's been through vision therapy to correct vision challenges due to muscle weakness (which showed up as a huge dip in processing speed on her WISC)... my adult relative realized through learning about what my dd has been through that she is probably still having fall-out in her vision due to her history of strabismus, even though it appears on the surface to be corrected.
polarbear