The biggest clue was when I started cutting off bits of the model. Even when all I had left was just the curved top of the dome those pesky triangles were still there. At that point I opened the .obj file and spotted it.

Time to go and tidy up those sharp edges now. Maybe also increase the number of segments on the rounded bits to give it a smoother outline.

Thanks again to everybody who's posted replies here. This has been a most enlightening experience for me.

I'll probably repost here in a week or two, just for a final check before releasing the model (or if I run into any other major problems!)

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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).