for those interested, the second light novel has also been translated into English (it’s even available at public libraries in the U.S.). it has this arc in it, so it’s good if you’re feeling a bit impatient.
(the light novel explains Yuki’s reasoning at the end here in a bit more detail…she figures they only have to whittle away ten, maybe 15 girls from any scouting or attack teams before the entryway team calls a truce. basically the entryway team’s goal is “steal all keys” but her team’s goal is “make the number of players equal the number of keys”)