I really like how you put this. Is that what I see out of Byrne’s Superman? No. But I really like how you put this.
I also, for the most part, agree with your assessment on Zack Snyder’s take on Superman.
That being said, I have to point out the many, many similarities between Snyder’s Superman and the Post-Byrne Superman. To start, Snyder’s version of Krypton was taken directly from Byrne’s World of Krypton. Both versions of the planet cloned their children instead of having natural births which is why both Byrne and Snyder’s version of Superman were sent to earth in a gestation pod. Both versions of the planet are, mostly, negative portrayals of it.
Next, Snyder’s Superman infamously killed Zod at the end of Man of Steel. Similarly, Byrne’s Superman executed an alternate universe version of Zod, Quex-Ui, and Zaora in Superman #22.
Going back to your assessment of Snyder’s Superman:
I think I get your meaning there. When I watched BvS, Superman seemed conflicted and pained about everything he did as Superman. To take a specific moment, he rescued Lois from the warlord in Africa and then spent a lot of time after that looking pained at the criticism he took for it. What this reminded me of was the Post-Crisis Superman unilaterally crossing the Quraci border in Adventures of Superman #427 (which, to be fair, was Wolfman-not Byrne). Following those actions, Superman took a lot of criticism for it and it pained him in the same way the Africa controversy pained him in BvS. In fact, the combination of the heat he took from the Quraci episode and the guilt from executing Zod and co. lead Superman to have a split-personality nervous breakdown. It never seemed to me that being Superman and saving people was a pleasure to the Post-Crisis Superman much in the same way it wasn’t to Snyder’s.
There are other similarities I could go into, but some of them would be a bit conceptual. The three similarities I mentioned are the most obvious. Again, I like how you summed up how you see or want to see Supes. I’m just not convinced that was the reality of what Byrne’s Superman really was and I definitely see too many similarities between his version and Snyder’s for it to be coincidence.