I'm a bad experimenter, I should have tried that long ago. I finally made a Bb PVC whistle that (IMHO) sounds and feels much better than my Gen Bb! All I had to do was try wider bore (20 mm). Preliminary plan:
You'll notice the large-ish holes, which provide the louder sound I needed. This Bb has a powerful, strong sound; the tone is sweet yet slightly airy; and unlike my Gen Bb, the two bottom notes are solid and reedy. I slightly bevelled the fipple, as in low whistles. I'll record clips and publish them as soon as possible.
It's raining, so I know what to do this afternoon: a new whistle in A and a new "whistle-chanter" in Bb. Next week, the new plans and information will be published on my page - plus, there will be a little surprise.
Fellow makers, please try this at home and report if you can outperform a Gen Bb. Given its solid reputation, this would be quite a remarkable feat.