The only bits of info I can contribute and not to any data set, but
1. as long as it's done properly and not over or underdone, not a lot of difference in my opinion between induction and flame. The issue is the ability of the user to be repeatable and the brass temp to get to the right figure for the right time.
2. the only time I've known annealing to be actually critical for the points you mentioned is one rifle where for whatever reason the neck cut of the chamber seemed to be oversize or something else weird going on. Resizing whatever brass fired in that rifle without annealing resulted in very light neck tension, which gave erratic performance on target and the odd smokey firing. Annealing allowed a lot more consistent resizing and neck tension, and a much better SD. Oddly the rifle wasn't inaccurate. This was a unique situation though.
I too would be interested to see the results of a well-set-up investigation of this!
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