Ok spoke to the dev guys and got the index queries they used:
create index email_address_email_message_id on email_address(email_message_id);
create index email_message_email_folder_id_index on email_message(email_folder_id);
create index email_message_parent_id on email_message(parent_id);
create index attachment_message_id on attachment(message_id);
create index message_publisher_id on message(publisher_id);
These should be the only ones across the DB right now.
I agree that throwing more hardware at it will most likely make it less of an issue, but as I said, this never happened before a few days ago, even on the same hardware. Also just a note here: this particular server only serves content to maby 10 people in a given day.