The issues with activity finder have been known and acknowledged now for years. Despite promises the issues would be fixed before this event went live again, it has been cancelled. Here is what I suggest you do for the event.
1. When an account logs in for the day, award every toon on the account a hefty reward box. Also reward the account the 3 event tickets for the day. (Just assume their intent was to participate in the event on all toons, be sure to award all toons the extra xp for the random dungeon they would have received as well as the email with rewards for completing the random dungeon)
2. Award the standard reward box to any toon logged into the game for more than 30 consecutive minutes. (Just assume they would be grinding the event for boxes and this is a reasonable time to queue and complete a dungeon.
I don't think anything else is really acceptable at this point.