For those who might want to know. ...
I ended up adding products in a separate Parts category for each part -- the middle and base examples above; top being the fountain in the Fountains category. I had to do that because as mentioned above, the Canada Post module requires dimensions as well as weight, and attributes don't have those.
I made the Parts category not load in the list of categories (admin switch.) And I added two mods from thatsoftwareguy.com -- Combination Discounts and Buy The Set. The BTS mod requires the CD mod, the features of which I don't otherwise use at the moment.
Then, because I had set up to display the Buy The Set button for each fountain that needed it, I had to use a category specific stylesheet to ensure that the Add To Cart button wouldn't be displayed for those products. As described in another thread, just put #cartAdd {display: none;} into that custom stylesheet for that category.
The net result is that with a single click on the BTS button, 2, 3 or more products (really a product and one or more parts) get added to the cart all at once. And they all have their own dimensions and weights, so the Canada Post shipping module can get its act together.
At this point the UPS-XML module is not getting the boxes and dimensions and weight correct, but we're working on it.
Rob



