unless you have a high-temperature annealing oven, you
can't just smooth them with a pencil torch since they will chip from
unannealed stresses.

This is where you need to watch those women who do glass sculpture at
the fair. They use propane torches with the flame spreader to even out
the heat. Once you get a feel for it you can put a rolled edge on the
glass. Just watch your heat. Practice on a bottle you have a bunch of.

Are you speculating? You've succeeded on cut glass bottles?

I suspect the glass sculpture stuff is using a low-temp, low-expansion
glass that doesn't need annealing, like chemists use for tubing so they can
cut and bend it in the lab. Very different stuff from what ordinary
bottles are made from, which is cheap but requires annealing.