Been watching this, and had to chime in with some ideas.

I found about a dozen broken whisky bottles, but just the shoulder, neck,
and lip. They were 1889's and brown glass. Nothing special.

I made a jig for my diamond tile saw, and cut them diagonally, all equal,
with some shoulder left.

I then mounted them on dowels on a board, and filled the void with epoxy.
It is a fine looking hat rack.

If I was to do this, I would get a Dremel or equivalent and make a holder
for it. I would then make a cradle for the bottle, and then make a cradle
for the bottles. All of this would be adjustable for different sized
bottles. A follower and distance gauge would have to be figured out so as
to keep the Dremel wheel at a constant distance from the surface, and
vertical for a vertical cut. This would be a little tricky, as the cuvature
is going to change.

If you were going to use a core drill and just drill a hole in the bottle
from the side, essentially, you would have up to four separate contact and
pressure points, and just the right amount of pressure and lubrication would
be needed, or you have toast.

I think one could be made by a good machinist, and someone who is good at
math so that the bottle in the cradle turns true, and the Dremel keeps the
same distance from the bottle. I do think that just having one contact
pressure point would be better, and perhaps even diamond discs are available
for Dremel/Foredom/et al.

Keep us posted.

Steve