It's not something that would be particularly difficult on a mill (and remember I said a 4-axis machine; the fourth axis is a horizontal rotisserie-type armatur

It's not something that would be particularly difficult on a mill (and remember I said a 4-axis machine; the fourth axis is a horizontal rotisserie-type armature), provided that the thread is stopped before the join points. The internal thread only seems difficult; the right tool bit can easily cut UNC-type internal threads to a bit-length-limited depth, and a keyhole-type bit would provide the thread-end relief. The external can be cut with a standard round-point 60-degree bit, as long as you don't try to cut threads all the way to the shoulder (a flat groove between the thread end and the shoulder wouldn't harm functionality -- and would be a good place to stick an o-ring if the bottle is supposed to hold liquids).