From my conversations with support on Hosting24, this limit is a total of all emails sent from a script AND all emails sent through a forwarder AND all emails sent through webmail on proper email accounts.
Has anybody found a way to monitor the last two (and disable them if needs be) to avoid getting their account suspended, support just keep saying:
I am sorry but you will can [sic] only monitor the outgoing emails with your own scripts. We do not provide any monitoring scripts.
Alternatively, has anybody found a free (or very cheap) way to avoid this limit all together?