I'm afraid I'm not an instructor, but hopefully we can scare someone up to help you w. these questions. If you snoop around here, you should find a few threads about current instructors offering to teach K-12 teachers FREE of charge. You could probably help get more teachers onboard with their CHLs, more quickly, by identifying one or more instructors in your area who'd be willing to help out in this way.
While your school district might not be comfortable with immediately changing their policy to allow teachers to carry, it cannot hurt to have a growing number of teachers go through the training, get their CHLs, and represent a growing number of people in the district who will support such a policy change.
Please keep us posted on how it goes!