Cool idea, I haven’t tried that yet.
I think I found the article about the impact of screws on a trim ring, here’s a quote…
“Adding flux from an auxiliary screw will break the symmetry of the magnetisation cycle within the string so the results will depend on the local recoil permeability of the string at the various magnetisations produced by the magnet. I am sure that there would be a flattening of the measured peak but it wouldn't really represent the true flux density.
Surely the best result would come from simply increasing the magnitude of the alternating flux. Getting enough Ampere-turns shouldn't be a problem but the trim ring screw would probably have to be replaced by something with a higher saturation flux density. Losses in the core probably wouldn't matter as long as a reasonably sinusoidal flux could be produced. Mechanical vibration of the string might need to be suppressed.”
My head hurts.