In order to cut the bottle in the middle of its neck, I had to keep the bottle upside down. It’s shown in this post (Slim flower vase) how difficult it is to get access to the bottleneck when the bottle is in upright position. That setup had some limitations, however, it was useful for cutting jars.
It’s not stable, but it worked this time. Quite a nice line was cut, and I moved to the kitchen. Boiling and cold water cracked the bottle.
The first sanding disc I used was 40 grit. It took me 20 mins to complete that step.
I finished sanding with 3000 grit and started preparing the inner edges.
Polishing compound helped to get a mirror finish.
I removed the labels with white spirit, and then I washed the bottle with warm water and washing up liquid. Dried and ready to use.