I make a few bobbins for the rewind industry from time to time and they also have to make non cored coils, not as small as this but similar principle.

What about getting a bar turning part down to 4mm longer than your coil and threaded it M4

The can be any size within reason but the part next to the thread turned down to 9mm as I gather that's just a visual guide on the coil being full ?
This will allow you to wind onto a thin plastic or paper former which can then be removed after.
The ends can have a card washer fitted with a small hole in to locate the wire at the start and then be disposed of after winding. This does away with the tiny drill hole at an angle. not sure why you need two start holes as the end of the wire is going to be on the OD.

Length of coil is controlled by a 9mm diameter 'washer' threaded M4 and held in place by a lock nut to adjust length of coil.

Or am I missing something ?