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I agree with what you've said. I'll have to think about it for a while.
I did look at the case of a spinning ring and it seems stable. But I'm only using the Newtonian approximation, and you have to spin it at a speed that increases like sqrt(log(r)) so eventually that's invalid.
I changed my mind on the space-o-gel though, at least for now.
Nice idea with the spinning ring. With relativity it should be fine as long as light itself isn't pulled in when going in parallel with the ring.