
Scrying (lv3), Alyssa Graham, or Scroll of Secrets if taboo make Gloria to look encounter deck by trigger ability. All of those require exhaust, so that Gloria only use those cards once per round. After those cards are ready during upkeep phase, Gloria has no chance to trigger those ability until the encounter cards are totally resolved. However, if the encounter card initiates the skill test, Gloria has a chance to trigger those ability. This window is the key window if Gloria wanna to look all encounter cards for 4 players game. If no test will be initiated, another investigator plays A Test of Will (lv 0 or lv 2) to forcly initiate test.
If Gloria in balenced 4-player group, Gloria could focus on controling encounter deck. Even if Gloria only looks encounter decks, the group can be very safe & stable. Gloria doesn't need to consider Fight; the enemy is always drawn by fighter (or flexible fighter/evader). The clue gatherer could go alone without fearing of drawing enemy. If Gloria remains action, she could investigate with high or play event such as Read the Sign, Drawn from the Flame.
The key cards for encounter control is Scrying, Alyssa Graham, and Twila Katherine Price. Gloria could look 4 cards by Scrying. If 4 cards are ok, then place 4 cards. If 1 or more is terrible, then discard/seal one of those card. In this case, place 3rd encounter card which has a skill test. Then, when a investigator tests by 3rd encounter, trigger Alyssa to look final unknown card. Twila Katherine Price could save the charge of Scrying. If you want to save the for Scrying, you could take Scrying (lv3); in this case, however, Gloria needs horror soaking sources, because Scrying usually gives 1 horror.