The gap change is not just due the plates free play, but the geometrical defect. We can try to save the plates free play on anyway you want, but the pick up still can bite the reluctor when vacuum works depending on the shape manufacturer gave to the asembly. Two problems to attack.

I selected to make somehow a tighter stud on plate hole with teflon tape over, which wraps the stud easilly and allows the pivot to work, since teflon is soft and somehow "lubed". Its also cheap and what I had handy. Maybe having a machine shop around could be made something better? Bush/sleeve the stud and get it tighter on hole?

Can't talk about voltage and timming variations due the gap change. Don't think something to worry as far you are within specs. I just try to set 0.008 average.

I also mill a bit the pickup end to make it flat/parallel against the reluctor.

I also measured EVERY reluctor point against the pickup and milled a bit each one to get them equalized, because the reluctor pin can set OUT of the shaft center the reluctor itself, so the reluctor ends on the pin side can be closer to the pickup coil, DEPENDING on how tight fits the reluctor on shaft

Dunno if is clear what I told