Phil,
It's the "skimming" surfaces that Michael describes that is giving you heat.... Here's a video where I adjust some curves and cut your part.
So in the video you see me "raise the bottom curve" by a very slight amount, so it's not barely skimming through the entire bottom of the chair. The vertical curve is adjusted but you cant see it in the video. I used my "super nudge" command which moves .01mm. So I moved that vertical curve .04mm deeper into the solid to get a clean cut....
"""""""""""" I don't know if I should have approached this differently..."""""""""""""""
What you can do in the future, is model the veronoi with the base "much deeper, or thicker", then in this Boolean operation, cut the back to specs with your curve. Booleans are good to have a "complete intersection".............
> I don't know if I should have approached this differently...
Well, the thing Burr mentions about having pieces that punch just partway through the other rather than skimming would have helped...
Also it would usually be good to do the boolean before doing the flow instead of doing it afterwards... But in your case here it's a bit more complicated since you have 2 pieces branching off in different directions, so I'm not quite so sure.
@BurrMan (and Michael) - Thank you so much for having taken the time to share your knowledge on these issues. The various explanations and the excellent videos really helped me to understand (a little bit) more about what I need to do to finish this model. I am very, very grateful!