I assume if you go to the tightest hole the gap goes away, but it's not comfortable?
If so, I think it may depend on how the existing holes on the standard size side line up to the clasp on the short side strap. I had the chance to try both before buying my watch and I noticed the holes are not in the same place, the holes start closer to the watch on the short version.
So if it aligns in a different way, it may close slightly tighter to eliminate your gap and still retain the comfort. However, if it aligns exactly the same, then you'd still have some gap, but less overhang from the end of the inside of the clasp. So I do think you'll at least eliminate the overlap bulk and perhaps close the gap some depending on the alignment of the holes to clasp.
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If you do buy an extra bracelet, I'd be very interested in the result!
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Seems our wrists are similar in size but probably different in shape. I wear my short bracelet on the same holes as you did. Normally on the 4th hole, which gives me a nice fit and comfortable enough but not super comfy like it seems to be for others. One hole looser gives me a gap on both sides, but it's a balanced look, which I prefer to just a bulge on one side. On hot humid days I sometimes switch to the looser hole for better comfort, despite not liking the gap look.