Still, I like the idea of being able to choose your mandrel diameter independently of the slot size on a given coil head, so I may pursue this matter nevertheless.
Alternatively, you know, perhaps a sleeve or spacer of a smaller dia. i.d. such that you could fit over a 1/16" or metric 1.6/1.8mm screwdriver or other bit would work. I certainly will keep my eyes open. But I think your original idea has merit. Such a sleeve or bushing with the right i.d./o.d. would be very helpful over a bit that fits the slot to bring down and stabilize a larger coil during assembly.
Good luck!