Union organizers approached national board after they say the school gave them the cold shoulder.
School attorneys argue the board is a political subdivision of state, not subject to federal oversight. That's counter to an earlier argument.
Larger-than-usual paychecks were cut recently, then they were taken off next payroll.
Members say they want faculty members to decide the issue through a vote.
SciTech Academy said faculty member stopped working there the day after the alleged incident.
The next move is up to the union organizers.
Two people will visit the schools on one of the days of testing next week.
Orleans superintendent, other education leaders also discuss unification, transparency at forum
Leaders of 20 charter-school organizations pledged to hire outside monitors to oversee all four days of state testing, but it appears that most will pay for only one day. Further, none of the charter groups contacted by The Lens sought competitive bids for the work, which school officials said could run up to $4,250 per day per school, most of which will go to one company.