Actually, a body with a thicker wall and a narrower bore, coupled with a head that is capable of supporting a larger bore, will also favor the higher register - which I think is more the case with the DX203. A longer window (as relates to the whistle length-wise) can also favor the upper register, but this is because when you move the blown edge further from the windway exit, it requires more air overall to produce a tone, which makes it more prone to wanting to play in the upper register.
The idea in tweaking some whistles, is to actually
shorten the window, while also changing the angle of the blown edge, and it's alignment with the floor of the windway to keep the air requirement about the same, thus optimizing the way the head splits the airstream, and reducing the resulting turbulence that is created as air enters the tube. The alignment between the blown edge and the bottom of the windway floor (think of this in terms of vertical elevation) ultimately has the greatest impact on balancing the two octaves - especially with regard to the tone of the whistle. A narrower window (as relates to the whistle width-wise) produces a more focused airstream, but will usually have lower air requirements (thus, it is better-suited to a narrower bore). It can give the whistle a sweeter, more pure sound through both registers, at the expense of overall volume. - Although I have an older sweetheart whistle which completely defies this point on narrow windway -vs.- volume that I have just stated, but this is a conical bore wooden whistle. To go into that would only confuse the matter.
One of the things I am most concerned with when I alter (or make) a whistle, is the difference in tone (or overall sound) between the upper and lower octaves. Having a strong low end and a thin, shrill, and/or raspy high end is no good. Having a sweet upper end that you can really push and a weak bottom end that is overly prone to flipping is no good. In other words, I don't like a whistle that requires a
major change in breath control from one octave to another, or that produces a radically different sound (tone) from one octave to the other. Another thing I am equally concerned with is cleaning up any random "ghost harmonics", squeaks, squawks, and undertones.
...and honestly, I haven't found any of these things to be a problem on any of the Dixon whistles I've had. They have breath requirements that are somewhat characteristic to them, IMO... So did the older Copelands - but nobody rushes to "fix" those, do they?
My own opinion on the DX203 is that it's a fine whistle in it's own right. The balance of the whistle when holding it is goofy. I don't like the thin ABS head on the heavy brass body. I think I would have preferred the whistle to have been constructed with a delrin head instead. - And yes, it is loud - it was made that way intentionally.