I get what you're saying. I might be trying to play ZSS too much like G&W. What would you recommend instead?
Obviously take all this with a grain of salt until someone else confirms what I'm saying, since I'm still not fully convinced that what I'm saying isn't just my personal play style caused by playing sheik, a character you're supposed to avoid jumping a lot with.
First thing I'm going to say is that what you were doing was working. You would jump, he would try to hit you, and then you'd punish on the way down. Assuming this isn't just the way you play with this particular person, however, it's not a good habit to have.
It looked like you'd jump because they would start closing in, and then you'd feel pressured, and then rather than deal with the pressure you would try to escape. With nowhere else to go, you went up and over. This is more understandable with 3.02 Zamus who lacks a proper grab, but the current iteration is much better at holding her ground. Even with old Zoot, you'd generally be using paralyzer to keep them at bay, though obviously this is not as good an option (though still plenty good imo). I don't know a lot about Samus but I'm pretty sure she doesn't have many great approaches, so if she's closing in on you, you should have the advantage. Just be wary of grabs and you should be fine. Dash dance to bait an attack, shield grab whatever approach she makes, or even just challenge her with a shuffled nair or paralyzer shot. My personal favorite counter to an approach is wavedash back > Dsmash; it's not the best since it can be punish by faster characters, but it's a great mix up, and against slower character's it's plenty doable so long as you don't become too predictable with it.
Another thing, you should take advantage of your grab more. You seem to be playing as in 3.02 relying more on your aerials and paralyzer to start combos. There were a bunch of punishes that you failed because you tried to shffl nair and it missed or came out too late. What with the nerf to nair that's going to happen a lot, but with the new grab you don't even need to use nair. Just remember you have a normal grab now: Run up and grab them.
Lastly, use Uair more. As I mentioned earlier, Nair isn't what it used to be. Not only is it not a great approach, but it's also kinda hard to convert off of unless you know you're going to hit. The angle of Uair was changed so it's kinda like a Falcon Uair, so use it like one: combo them across the stage with it. Nair is more useful mid-combo now.
That's all I got. I'm pretty confident about those last two paragraphs, it's just the first part about jumping that I'm wondering about.