Two PROCESSLIST/STATUS samples taken ~30s before and after the slowness started show that all of a sudden ~1300 connections are in "Opening tables" status. This continues for the next ~6 minutes, then the number goes down again (probably due to failing over the write virtual IP to the other cluster node).

A gdb backtrace taken at about 6 minutes in shows 242 connections waiting for a mutex in tc_add_table_callback(...): mysql_mutex_lock(&element->LOCK_table_share);

Unfortunately there's no PROCESSLIST snapshot close to the time the backtrace was taken, about half a minute before the "Opening tables" status count was still at ~800 (down from ~1300 for the first time), ~30s later it was down to zero again.