That's very useful and well illustrated, John.
The new pics of the rim leave me doubting a bit - it does look rounded, and johngowan says he tried using his tongue to test for edges.

(Which is not remotely disgusting. It's eminently sensible, and I know of others who lick glass to test it. You test for real pearls by rubbing them on your teeth.)
But there is that peculiar flat-looking ring in it. That doesn't look right. I'd really like to be able to get my teeth onto it too, and check it myself.
As it is a very unusual thing, and has the pawmark, I imagine somebody may well have paid for a very good repair job.
I've found myself in the opposite situation. I bought a lollipop at a National which was far too cheap. The seller said she thought the top was broken. It wasn't. It was raggedy but very tall and all properly heat finished.
I've found a pic of the bottle i think is the artillery shape. I don't have it any more and I don't have pics of the rim, which is rounded and heat finished. It didn't look peculiar or odd, I don't think.
