I used WP-DB-Backup (https://wordpress.org/extend/plugins/wp-db-backup/), which can export all the tables specified, to successfully export — and re-import via the phpMyAdmin panel — the whole megillah, including BP-specific data.
I seem to be having the opposite experience of everyone else: in a clean install of WP 2.9.2, the Events submenu shows up in the nav bar, but all the links lead back to the front page and there’s no apparent event-related control panel on the backend.