Thank's for the details and the links, Frank.
I am now having recollections of reading something before about the "questions put to a proponent of the cutting theory". I had forgotten about that. Most of what is said in Rosemarie Lierke's 2004 webpage article makes good sense to me. I can therefore accept the "two-shelled blank" explanation. The parts that I don't quite follow are probably because I don't properly appreciate how the outer wall network was formed in order for parts to be removed at the correct positions.
But even if the two-shelled approach was the method used by the Romans, it still seems clear that the outer cage and the support struts were finished by cutting, including some possible undercutting.
In the thread on "Paperweights" my analogy to the Chinese "balls-in-balls" can now be said "not to hold water" (both figuratively and physically

). And yes, the actual technique used for Barry Sautners's work is somewhat different.
What I still find intriguing, though, is the (apparent or real) lack of acceptance by some authorities of anything but the "cut thick-wall" process. I assume this is the reason for Bonhams blurb to stick to the long-standing line. And it perhaps also explains why the
Glass Cone article, which was based on much of the Bonhams commentary, and focussing on the "cup vs lamp" idea, gave no alternative views on the procedure.
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If anyone gets a chance to visit the Glass Musem at Jelenia Gora in Poland, they have a very nice example of a modern reproduction of a "cage cup", but unfortunately I did not get any information on it when I was there.