This is very interesting. I hate to post such long messages here, but I wanted to share with you my observations. I saw 4 strengths in your post. Lyc and Calc being the strongest followed by Sulph and Arg-n.
So I printed up the pages from my MM and started highlighting all the characteristics that match each rememdy. (And marking red on any adverse matches.) Then in Relating the remedies to each other I saw an interesting pattern.
First, the strongest match overall was with the Sulpher. He matched in the overall Character description, Mind, Ears, Nose, Mouth,
Stomach - esp loss of or excessive appitite. Drinks much, eats little, Milk disagrees, desire sweets, 11:00am needing to eat.
Adomen, Rectum,
Urine - particularly the sudden call to urinate with great quantity of colorless urine. (a big problem when going places.)
He wets at night.
Respiratory - brown spots all over chest (I'm not sure if that mean the developing moles which are very brown.)
Back, Extremities, Sleep (always wakes up between 2 and 4am to crawl in bed with us.)
Skin - which he always has pimply pustules on his cheeks.
The Modalities - in particularly the better from lying on right side, from drawing up affected limbs.
But in each category there were a minimum of three or more matches. Except in Head, Eyes, Throat, Male - there were none.

The second was Calc. Carb - not as profound as Sulpher. But in Mind there was almost and exact match. The within each catagory there were a minimum of 2 matches each. Except for Eyes, Ears, Nose, and Face. But there were some key areas that struck me.
Ears - perversion of hearing, hardness of hearing.
Mind, Head - worse from mental exersion.
Throat - had tonsils and adnoids removed do to excessive swelling.
Stomach - craving for sweets, milk disagrees, loud belching (constant problem.) The stomach matches almost exactly.
Stool - large and hard.
Urine - Abundant.
Back - Pain between Shoulder-blades. Nape of neck stiff and rigid.
Modalities - worse from exertion, metnal and physical.

The third was Lyco. Where as the digestive disturbances and mild temperment, earthy complexion, right sidedness, worse from 4-8.
Intellectually keen, but of weak muscular power. Sensitive to noise and odor.
The mind was again the strongest match - and especially in regards to confused thoughts, spell or writes wrong words and syllables. Can not read what he writes. - This is where I see the affects of the Asperger.
Beyond that only a few matches on the other catagories.
Eyes - day - blindness.
Ears - deafness
Nose - sense of small very acute
Throat - food and drink regurgitates through nose. (Big problem since adnoids removed.)
Stomach - Aversion for Sweet things.

The forth Arg-n I'm not going to mention for reasons I'll explain in a minutes.

I feel that I was reversed in my orginal concept that he was a plant by constitutional which was being inhibited by some organic compound.
What I see that is that he is of an organic compound, inhibited by a plant matter.

In comparing complementary relationships, antidotes and compares: What I noticed is that both Lyc and Calc work best after Sulpher. That Lyc acts as a special benefit after Calc and Sulpher. That Arg-N has no relationship to the three, and the matches weren't very clear cut as the others.

So what I feel that would work best is to
Start with Sulpher, follow with Calc Car,
then finish with Lyc.
At this point I'm not sure of potency or duration. Whether doing 200C - maybe one each over the next three months. Or if the Lyc might be best as a low dose as the symptoms are of the illness nature, but the Sulpher is of the consitutional nature.

Please let me know what you think.