If I run up to a mob and cast a non-instant, frequently one of the following toons is still moving, which prevents the spell cast.

Pausing a moment before casting might help you. I doubt its something this simple, but start with simple fixes and move from there.
Having A/B or A/C or B/C cast, but not the 3rd is very weird; if it was always B not casting then it would be B's assist macro.