@Shard, maybe we should have Ridcully rest? If they start summoning the First Circle Archangyl we'll want to have its True Name on hand so the Grey Knights can banish it before it does too much damage. Given the time constraints we're operating on and how it'll take multiple turns to get the True Name, we'll need to have him rest this turn if we want to succeed in this. Here's the two timelines assuming it'll take 3 turns to get the True Name (Third Circle is 2 turns).
0. Ridcully helps with the bluff at exhaustion level 1. Ridcully is now exhaustion level 2.
1. He rests. Exhaustion level 0. First Circle is 0-2 turns away from summoning.
2. Ridcully is 1/3 of the way to getting the True name. Exhaustion level 1. First Circle is 0-1 turn away from summoning.
3. Ridcully is 2/3 of the way to getting the True name. Exhaustion level 2. First Circle has been summoned by now for certain.
4. Ridcully is 3/3 of the way to getting the True name. Exhaustion level 3. First Circle is banished.
0. Ridcully rests. Ridcully is now at exhaustion level 0.
1. Ridcully is 1/3 of the way to getting the True name. Exhaustion level 1. First Circle is 0-2 turns away from summoning.
2. Ridcully is 2/3 of the way to getting the True name. Exhaustion level 2. First Circle is 0-1 turn away from summoning.
3. Ridcully is 3/3 of the way to getting the True name. Exhaustion level 3. First Circle has been summoned by now for certain. First Circle is banished.
In the first timeline, the First Circle can be in the Materium for up to 3 full turns without being banished and a guarantee of 1 full turn without banishment. In the second timeline, the First Circle can only be in the Materium for up to 2 full turns with no guarantee of having a full turn without banishment. Snowball theory and the possibility of the Archangyl not having ANY full turn on the Materium without banishment lead us to conclude that we should have him rest this turn. We have Valinor's plans, Frederick is Paragon Martial, and he'll still have the help of a full divination choir. Ridcully won't be necessary for that. What Ridcully is necessary for is getting the First Circle's name as no one else can do that.
Note: Daemonologists can slow down the ritual, but to what extent they'll be successful is unknown. They might only slow it down for one turn, which in either case would still give the Archangyl the possibility of a full turn without being banished. I could also be lowballing the time it'll take to get the name. It could take longer, maybe 4 or 5 turns total. Given that the on the 3rd turn he'll already be getting the penalty of exhaustion level 2 - which is significant - he'd have to take a turn's rest before doing that final 1-2 turns of scrying. Reducing the time it'll take to get the True Name by even a single turn could easily be crucial, especially when you consider the times in this quest when very important rolls succeeded by a margin of only 1 or even 0.