I wonder if the diamond blade on a wetsaw would do the same thing, and in the blink of an eye? When I hand-cut specialty pieces of tile it's kind of messy because the gate is up, but that's how you'd approach cutting a bottle. I wear safety glasses and ear protection. Throw in a pair of heavy-duty gloves, and see if you can't cut that top off by touching it down to the saw as you slowly turn the bottle. Of course, a wet saw starts at about $100 for the Home Depot variety. Dremel is more portable (but probably slower since it is smaller and you are holding the tool in one hand and the bottle in the other. With the wetsaw, you're holding the bottle with both hands and have more control).

SRS