Got it, thanks for the example!
First, I like a system like this.
Second, I would still have the attacks "deal damage". One thing about Hit Points being abstract is they can represent a creature's decreasing morale. In your example, the first attack disarms the giant (the damage is demoralizing for losing its weapon), the second shoved down (the damage is knowing you are more vulnerable), and third shove back (damage is the giant is pushed out of position and increases vulnerability).
Since "hits" don't have to actually hit (the damage is the target avoiding lethality), I think such a system still works. With cumulative hits, the pressure against the target mounts, allowing you to do more "impressive maneuvers/effects".
Well if hits that deal damage continue the chain, I might have to increase the number of hits to do effects. On not since your chain can be ruined by rolling a 5.
Any ideas for the missing Dragonstrikes' effects? I made all the Metallic ones based on their secondary breaths. But I's stuck on the Chromatics. I was doing it more based one the dragon's personality (AKA big dumb white just deals damage). Might branch out to a new thread.