One more thing I just want to address.
So if an early effect pushes my model into a disengage trigger, wouldn't I disengage at that point?
In theory, yes. But the "early effects", i.e. the special effects from the damage tree, never do any damage themselves, so they cannot possibly trigger a disengage. Pushes and repositions and other damage tree effects all affect placement (which is where you have the possibility of the attacker moving outside of attack range), or add fatigue, or give you favor. Once you have resolved all these non-damage effects, the early effects, then you apply all the damage in one go.
The only way I can see what you describe as being possible is if I push a Zephyri model into a wounding hazard. That inflicts an immediate 3 damage when the push happens, so if those 3 separate damage trigger a disengage box, then the defender would be able to move away in the middle of the attack (I assume), and not suffer any of post-push attack damage. But that's only possible because the 3 damage from the hazard are separate from the damage from the actual main attack. The main attack damage, i.e. the damage from all the damage tree results, is all applied in one go.
(Note that I had not thought of the wounding hazard -> disengage thing before, so I don't know if it works in reality - but I don't see why not.)