First thing I believe you need to consider is that Shun knives, the Premier in particular, are actually German knives, though made of Japanese steel. They have a lot of belly in the profile, and the point is way too high to be practical, it literally "shortens" the knife by making the tip end mostly unusable. They are also thick behind the edge, usually .025" or more. This increases effort, which reduces control, and is likely responsible for you steering issue. Japanese knives have a flat or nearly flat edge for half or more of the blade, and the tip remains below the bottom of the handle. A knife in the dollar range you are considering would typically be .010 at the edge, or less. At cutting they are like night and day compared to a Premier.
As for sharpening, I doubt if many, if any, Shun knives were delivered at 16deg/side, the buffing job they do removes considerable material from the edge, in the wrong direction. And their free sharpening is much worse.
You will absolutely need to learn how to sharpen and thin your new knife. Send it out to ANY sharpening service, or put it through one of those motorized units, and in no time your extremely nice $200+ Itonomon or whatever, will be cutting more like your Shun.
These are the facts, regardless of make or cost, all blunted and dull knives are pretty much equal.