Amount of times you’ve been able to neck size a case before it becomes too snug to chamber? And when it does, how far to you set the shoulder back to get it to chamber again?

Depends on the round, case manufacture, and how hard you are pushing it along with if it has been annealed etc.
I don't think there is a hard fast answer.

By annealing necks I’ve been able to go 10+ loadings using only a LCNS with no shoulder bump necessary.

I’ve gone 10 firings on my AI cases pushed pretty hard. Full length sizing die, just “kissing” the shoulder.....never annealed! I had a case separation just forward of the web, after the 10th firing. I now dispose of my brass after 10 th firing. memtb