Your 1200/1600 ceramic hones might be a good tool to do it. I usually use a medium Spyderco hone (brown) for the same thing. Some very light edge-leading passes, at a slightly elevated angle, will often help to remove the wire, either by filing it down gently, or by breaking it off. The wire will likely fold to one side or the other. Check for it, by using your thumbnail or needle or toothpick, by sliding it down the face of the blade, toward the edge. If the wire is folded over, you'll run into it on the side it's folded towards. Either way, getting rid of it is the goal. Make a few passes (maybe 3-5), on the side it's folded to, and keep re-checking for the wire as you go. You'll likely need to 'chase it' from side-to-side, as it folds back & forth. Eventually, that repeated folding over & honing should break it off, or file it away. So long as you go about it patiently and gently, you'll get it fixed.
For clarification, when you say you gave the knife a 'quick rub of steel', are you talking about using a chef's steel? If so, and if doing so changed the cutting performance significantly, that pretty much confirms the wire edge.