I would offer a few perspectives:
1. DSM-5 criteria for learning disorders are not universally accepted, and in fact, there is considerable disagreement with them in the LD field. The ICCD (international diagnostic standards) is more in alignment with the position of many of the leading researchers, and takes into account achievement expectations based on ability, not only normative expectations. So even if this doesn't meet DSM tests for LD, it may meet ICCD criteria (which, btw, are still the diagnostic codes used by Medicaid and Medicare).
2. Regardless of which medical diagnostic standards are used, educational disability has its own standards, with mostly overlapping federal, state, and local standards. Federal standards allow the use of either normative weaknesses (typically in RTI states, and typically - 1SD, or below 85 standard score/16th %ile) or personal weaknesses (typically in severe discrepancy states) to be used as the criteria. States have made their own decisions as to whether either or both of these standards may be used for determining special education eligibility.
In your child's case, the severe discrepancy definition might be applicable, but the normative weakness one likely would not, with some exceptions. OSEP guidance on ADHD in particular (but this is actually applicable to other disabilities as well) has stated that eligibility decisions cannot be based purely on grades or achievement scores, but should also consider the effort and time expended to attain those performance levels.
3. I am struck mainly by the marked difference between verbal/auditory tasks and nonverbal/visual spatial (including processing speed, rapid naming, and digit span backward, which is often associated with visual memory strategies) tasks, a difference which is not restricted to motor-involved tasks (though fine motor does appear to exacerbate the weakness a bit).
The cognitive profile is borne out in the achievement scores, with the weakest areas (pretty comparable to visual spatial cognition) in math computation and especially math fluency, which aligns with the rapid naming relative weaknesses and fine-motor processing speed. Interestingly, oral word fluency, which is a retrieval fluency task using a meaningful semantic cue, was much stronger than the fluency tasks using rote or linguistically nonmeaningful materials.
4. The IRL concerns you list are largely ones that are found in the Tourette's population, so you don't necessarily have to reach for a new diagnosis to explain them. But comorbidity of Tourette's and ADHD is also very high (63%:
https://www.cdc.gov/ncbddd/tourette/otherconcerns.html), so that might be an avenue to explore if there are treatment options you would consider. The same source found LD comorbid at 47%.
5. If your child is already on an IEP, it should not matter what eligibility classification is listed; the IEP goals and services should be designed around the child's identified needs, not locked to the named disabilities.
