The whole building crawls while HSRP flaps on the distribution switches

At 14:05 users across the building report the network crawling, then dropping. HSRP on DSW1 and DSW2 logs state changes in several VLANs, SSH to DSW1 takes 20 seconds to answer, and monitoring shows DSW1's CPU at 99%. The campus runs Rapid PVST+, and DSW1 is root and HSRP active for VLAN 30, the third floor user VLAN. A meeting in a third floor room started at 14:00.