Good day.

Thank you for the detailed post as it does help me at least to understand what is going on.

Abilify is one of those neuroleptics (antipsychotic is a very outdated term) with mood stabilizing effects, but is activating. This means that unlike the more sedating ones, it actually gives some energy.
With that effect, it is often used in treatment of depressive-type episodes because of how it is able to lift the mood.

Quetiapine is a more sedating AP and therefore stands as one of the first line treatments of acute mania (along with olanzapine and risperidone) and should thus have a calming effect on agitation or other manic symptoms.

In my own experiences. I was first placed on Abilify after suffering an acute manic episode a couple of years ago. Zyprexa was what the doctor used to bring my mood down with the unpleasant sedation effect, which is common in Zyprexa.
Abilify seemed to work. Odd enough. The only problem was the agitation it seemed to cause. it was from there that I was placed on quetiapine.

My experience with quetiapine? Definitely calming in comparison to Abilify. I had tapered up from 25 mg to 200 mg of Seroquel. Funny fact: quetiapine has a paradoxical effect in which lower dosages act more as an antihistamine, thus causing drowsiness. The mood stabilizing abilities of the drug start at higher dosages- not entirely sure, but definitely higher than 100 mg.

As someone has pointed out, anticonvulsant drugs are useful mood stabilizers:
Lamictal, Depakote, Trileptal etc.
These tend to be chosen for long term mood stabilizing because of the side effects of neuroleptics such as quetiapine and so forth.

Lithium is another one, but I wouldn't go there unless you really have to. It is a very old and very efficient drug if you are able to tolerate side effects.
I am not sure whether you have ever tried him on risperidone? It is often used for agitation and manic-like symptoms.

Hope this is somewhat helpful.