I understand your point. But I also think that the concept of hemisphere dominance is a tricky question.
For the term ambisinistral, I came across it earlier today, in the context that some left handed people take issue with it, due to the use of “sinister” for the left hand, and the negative associations that go with it. As you say, ambidextrous means both favorable, showing the historical thinking of dexter (right) = good, and sinister (left) = bad. I don’t know if there are any non-judgmental terms to describe those situations.
As an ambidextrous person, do you play bass or guitar with either hand? Or do you prefer one for stringed instruments?