In the spirit of NEVER leaving anything alone,
I used a piece of 10 GA. solid copper wire instead of the tubing,
Reducing the coil diameter to just outside of the ceramic insert (MIG welder gas cone),
The time didn't change too much, came in about 28 seconds, still using 24 volts DC,
But the results were MUCH better since I turned the coil sideways to control the depth the ceramic insert/stop allowed the case to enter the coils.
Don't know if you can see the annealing color change on the neck of the case, laying on the table, but this REALLY worked out for getting the annealing where I wanted it.
With solid copper, you MUST switch the induction unit On/Off between cases to allow the coil to cool.
Left on continuously it would eventually melt the copper coils.
This is no issue at all for the guy wanting to anneal one case at a time, no automatic feeding system.
The next step is to find some copper tubing I can reduce coil size but still run cooling water through...
Maybe 1/8" tubing, just larger than a 10 Ga. wire...