Nice comments Jante.
If you think about it, the actual servos/steppers can be a long way from the swivel point at the mouth of the bottle, giving a higher reduction in errors at the business end. ( my paper napkin wasn't very big 
)
To get maximum printing area the swivel should be at the mouth of the bottle.
I think the base mat can be printed from the same material first, and stuck to the side or bottom of the bottle ( it could be waves on the sea , whatever )
The tubes I see as 3 sections of tubing from radio telescopic antenna, with the middle diameter one replaced by some mica insulation , It could be brazed / soldered at the end, and a hole drilled.
I have a vague notion of using 5 sections of the antenna, with another tube on the outside with an air gap, sensing the tube touching the glass side of the bottle flexing the "proboscis " as a sort of end switch.
These are all just thoughts as I drill 50 square holes in plastic boxes while all around are enjoying a holiday !