Solution: National Air and Space Museum
Answer: MAIDENVOYAGE

Written by Josh Batkhan, with ideas from Dawson Do. Art by Dawson Do and Ryan Thomas

Each shape can be grouped using the number of edges. The Asteroids theme suggests that these shapes were once a single larger asteroid. Combining the shorter words and unscrambling them gives the name of a NASA shuttle.

These shuttles can be ordered by the number of edges of the original shape, then indexed by the player score to spell the answer: MAIDEN VOYAGE

Edges Words Shuttle Letters
3 CUBA, LIMO COLUMBIA MAI
4 REED, UNOVA ENDEAVOR DEN
5 DICE, SOY, VR DISCOVERY VOY
6 CLAN, HER, LEG CHALLENGER AGE