Why do you feel the need to step backwards? I'd leave the initial sharpening, do the resize to 2048, then if more sharpening is needed for web, apply it.
It is almost impossible for banding to exist in a SOOR, unless you BADLY under- or over-exposed the image, which you didn't do here.
So this indicates a problem with your screen. Is it an iMac?
How new/old is your computer?
Second question, do you have another computer (even a laptop would do) that you can temporarily plug the screen into, to see if it bands then too? We need to pinpoint where the problem is coming from.
Ok, yes, that was the same on mine.
All right, that proves to me that there's no problem at the interface end. So it must be at the back end.
Tell me, what kind of cable do you have connecting the screen to the computer?
Ok. Now go to Edit>Assign Profile. In the drop-down menu in that window, I want you to briefly try every available profile option.
They will make the image all kinds of wild colours. I don't mind about that. All I want to know is if any of the profiles make the banding disappear.
Ok, let's continue using that photo to troubleshoot. Further down that page is the download link for my PSD file. Can you download it and open it in Photoshop, then let me know when you have done so?