OK, so I spent some time paying attention while playing around with this rather than relying on what I recall while out on the water. A few notes:
1. When the throttles are in neutral, the boat doesn't move through the water. My statement that my boat must have been biased slightly in reverse was not correct. The reason that I thought that it was is that it's the trick that I tell my brain in order to predict what the boat is going to do while in neutral. It behaves like it's in reverse while in neutral from a steering perspective. In neutral, while not actually moving through the water, if you turn the wheel right, the stern will move right, but the boat does not go forward or backwards.
2.
@Cobra Jet Steering LLC and
@jacoviii are correct. I should have done more than glanced at what they said before replying earlier. The shape of the new buckets, the relative motion of the nozzle and buckets is the reason for this behavior. While in neutral, with the reverse gates adjusted properly, when the steering is centered, the drive output gets split more or less evenly between the two have of the bucket, with one half directing the water down and somewhat to the left, and the other half directing the water down and to the right, and you have no yaw input introduced to the boat. While in neutral, when you provide right steering input, water is directed left (and down) with the bucket in the neutral position. Opposite for left steering input. This is all (I think) a byproduct of how the nozzle / buckets need to behave for spin mode and lateral mode.
3. @fsh 20 sport is also correct (as usual) regarding adjusting neutral. Breaking out the manual, the reason for needing YDS is so that you can command neutral with the engine off. The procedure that is outlined involves first checking the adjustment by measuring the distance between the two adjustment nuts. There is no reason that you can't just go ahead and make whatever adjustments you want.
All this to say that it is evidently "normal" for the controls to behave the way that they do in neutral. So long as you know it, it really is no big deal. It's way easier than what everyone has to deal with on Waverunners in reverse since while in reverse, the boat acts like you'd expect.