This is a legislative fight.
You need to find out who the allies are and who the antis are.
You also need to understand how the process works in NM.
You need to understand who wrote that policy, how the policy got started, etc.
IMHO the charter school movement coalition is an extremely broad one. Properly organized and with the right information and targeting the right people, you'd be successful.
I know that in Texas that one-on-one meetings with legislators works very well. Groups that can motivate polite, well-reasoned, and well-spoken people from each legislators districts to meet with that legislator do very well. If you can get 50 people from EACH legislators district to meet their legislator on the topic one-on-one while generating a few white papers laying out why the new proposed policy is not better, then you have a very good chance of winning.