Largely that, while I think you have the timing issues okay (in the sense of when something can happen in the order, not necessarily on exact timing), the issue is that the rules clearly say that instantaneous spells cannot be dispelled. I appreciate the logic that went into your argument, and the thought behind it, but I don't think that it rises sufficiently high to counter that rule, even if the rule doesn't make perfect sense (which ones do?).
All of that said, I'm making that statement on the basis of what I think the rules say. At my table, though, it would work pretty much like you describe. I'm not going to offer it to the players as an option, but if one asks if he can do it, I'll say yes.
I think there's a couple of questions to be had about that.
Huh. Actually, re-reading:
"Many spells are instantaneous. The spell harms, heals, creates, or alters a creature or an object in a way that can't be dispelled, because its magic exists only for an instant."
This doesn't say that the
spell can't be dispelled, exactly. It says that the spell "harms, heals, creates, or alters a creature or object in a way that can't be dispelled". Which is not the same thing as "the spell itself cannot be dispelled".
One way of viewing this is "these spells cannot be affected by dispel magic, period, and this is why". The other is "these spells generally aren't subject to dispel magic, for the following reasons; if those reasons didn't apply, things might be different."
Consider, if you will, the hypothetical alternative rules text: "Spells with an instantaneous duration cannot be dispelled." No further qualifiers or explanations. Would that be clear enough? Sure. So what's the purpose of the explanation? In 5e, I tend to think that if a rule presents a justification, it's there as guidance for rulings. The goal is to tell you
why the rule is there, so you know when it will or won't apply.
Also, consider context and history. People frequently come up with the idea that they can dispel a magical effect, and then they look at a magical effect that has taken place, and they suggest dispelling it. This language tells you that instantnaneous spells don't work that way.
Now, here's a thing to consider. Can you dispel
call lightning? Of course you can. It's a spell with a duration. But would that dispel the damage done by it? Of course not. The key here is not whether or not the
spell is instantaneous, but whether the "harm, heal, create, or alter"
effect is instantaneous. And even though
call lightning does not explicitly state that, we understand the intent to be that the lightning bolts do damage which is instantaneous, while the spell continues for its duration. Dispelling the spell won't undo the lightning strikes that have already occurred.
(That said, I totally thought I remembered other wording that was closer to "you can't dispel instantaneous spells", but I can't find it at the moment.)