Surprise move comes as schools expected to lose money threaten to sue the state.
Officials at Mary D. Coghill and Fannie C. Williams voted this week to transfer from recovery district.
Schools would get more money for special-education students, less for gifted students.
Seven of their combined nine schools have improved enough to return to Orleans Parish School Board.
College will be out of reach for more Louisianans if state budget mess guts scholarship program.
Four others in the 10-school network were eligible, but move only would apply to Renaissance High.
State required the network to hire a consultant to comply with corrective-action plan after cheating.
The move to assign responsibility is in addition to the monitors the network pledged to hire.
State will pay for monitoring of state-chartered schools up for review. Other RSD schools will hire their own.
The move comes shortly after the Algiers Charter School Association fired its CEO.