I can't speak to larger districts, but this would certainly be a big challenge in smaller districts. I would think your best bet is to rely upon any connections you have. References alone are probably not going to be enough. If you can find an opening in a district where you have people that know you and are willing to vouch for you, then you have a real chance.

I have twice discussed with a superintendent assistant candidates who had issues in their backgrounds (no convictions). Both times the superintendent laughed me out of the office.