Yes, it is possible there is some connection between his history of poorer achievement testing and his history of lower processing speed scores. Among other things, processing speed is associated with automaticity, which is one of the core deficits in quite a number of learning disabilities.
It sounds like the social anxiety direction is one that is worth investigating further. Keep in mind that psychotropics are not the only way to go. CBT and related talk therapies have a track record nearly indistinguishable from anxiolytics, when implemented with fidelity. That would be a very reasonable place to start from in a child who is not severely incapacitated by anxiety.
The WRAML2 is a measure of memory. Did he do any differently on the verbal and visual measures? Some of the visual measures are also affected by fine motor skills.
The IVA is an executive function test, usually used for ADHD, that assesses attention and impulsivity.
I think additional testing, including achievement testing, is a good plan. I would want to tease out fine motor (OT) vs anxiety (or it could have been both on this round of testing), other visual skills (e.g., tracking), and subtle language processing deficits (weaknesses in pragmatic language are not found solely in ASD). Including measures of fluency in the achievement testing may help to clarify the impact of fine-motor/processing speed on academics.
Having good handwriting does not preclude typed response as an appropriate accommodation. Some dysgraphics have very beautiful handwriting, when that is all they are doing, but then have insufficient mental processing power left for other important tasks, such as spelling, and expressing ideas through language.
BTW, although not knowing that the tasks were timed is a legitimate possibility in his PSI scores, I should note that the standard directions say, "work as fast as you can without making mistakes until I tell you to stop," and the examiner says, "go," when the timer is started, so there are fairly obvious cues that the vast majority of students understand to mean speed is a factor. So not realizing that he was supposed to go quickly is also clinically significant data, probably related to pragmatic language.
