In reference to option 2 - I donโt see how arming school administrators disincentivizes suicidal people. Itโs obvious that dying is a big part of the point for many of them, which you go on to point out in option 3.
I think you make a reasonable point, but it's worth mentioning that most of them don't end up dying, they shoot until someone returns fire and then they give up. Returning fire quicker should obviously be a part of the overall package.