MIT Mystery Hunt 2020/Hat Venn-dor

Hat Venn-dor is a text-heavy interactive puzzle from the round of the 2020 MIT Mystery Hunt.

Puzzle Elements
Interactive (Teamwork Time) - The third Teamwork Time puzzle in the hunt. During the hunt, several people on a team could work simultaneously on a shared instance. This instance had a timer, requiring teams to work quickly.

Clue-Centric - With each Venn Diagram were six clues that needed to be answered.

Jumbled - The answers to each clue could be pieced together using the N-grams below each set of clues.

Something in Common - Each set of six answers can be arranged into the six outer spaces on a three-way Venn diagram using some set of categories. To complete the set, solvers have to find a word belonging to all three.

Enumerations - The common word is enumerated using a series of blanks...

Marked Spaces - ...one of which has a circle. Extracting the letters in these blanks provides the answer.