Okay, not quite there yet. But after playing around with some subdivision, sliding edge loops/vertices, and bevels, I think some light bulbs are glowing dimly in my brain. The new version of the dome with the square bit on top just looks so much better too me. And hey, who'd have guessed? Edge loops just seemed to appear! I think (and I'm often wrong, but maybe not this time) that the edge loops make sense too!

I've added regular exports of parts of my model as obj for examination in DS and Poser to my workflow. Yes,  I know it's obvious now!

I'm a little unsure about the triangle that appears in the bevel, where the dome and square corner meets (in the blue circle on the diagram). But I think that seems to be a triangle in its proper place.

Talking of bevels, I noticed that I can make the corner bevels on the base out of quads or triangles (the two images on the right). Is there any reason I should prefer one over the other?

Any views/observations on any of this?

P.S. thanks markschum. I think I'm going with bevels on this model, but I'll check out the commands you suggested - I'm playing with Anim8or now as well as Blender.

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The 3Dcheapskate* occasionally posts sensible stuff. Usually by accident.
And it usually uses Poser 11, with units set to inches. Except when it's using Poser 6 or PP2014, or when its units are set to PNU.

*also available in ShareCG, DAZ, and HiveWire3D flavours (the DeviantArt and CGBytes flavour have been discontinued).