What if the first level managers actually acted like an ExtremeTeam, instead of like courtiers cutting each others' throats for the attention of the SunKing? Together they would have stories, planning, pairing, refactoring (reorganization). If asked for help, they would have to say yes. They would set their own estimates. They would communicate directly with the customers' first level managers.
Might work, couldn't hurt, worth a try.