I'm not sure about the necessity of faking his death to have the freedom to act. Eb has been a Senior Council member almost from the start of the war, but it hasn't stopped him from secretly founding and recruiting a rebel force under the nose of the Council. That same force has met with other factions (Vadderung, etc) without the Council knowing, and Eb has run side missions with his personally selected Council squad (mentioned in DB, I believe) without any oversight.
Avoiding suspicion of working with the enemy also strikes me as an unnecessary concern. If he hadn't faked Archangel, he'd be in charge of the war effort, and would be all but beyond suspicion. If he faked it, and had only himself and a handful of his loyal personnel survive, then their presumed desire for vengeance would put them completely beyond suspicion.
I'm not seeing a real benefit to faking his death for those reasons alone. Are there any other reasons anyone can think of?
Would he need to do it for some reason to avoid the attention of other forces? (i.e. Vadderung, Mab, etc) Could his "death" have made a change to himself? One that would remove him from the detection of the Fates/Mothers, whom would otherwise know what he was really doing and could potentially reveal him to the Council if they learned he was using Outsiders, and therefore treading on their purpose?