Have you checked out this option:
Percentage of email messages to queue and retry for delivery
This configuration option allows you to define how overages are
handled when a domain exceeds the maximum number of emails allowed per
hour. By default, additional messages are queued for delivery and sent
in the next hour. This option is only available to the root user and
to resellers that have root privileges. The configuration data for
this option is stored in /var/cpanel/cpanel.config.
The value you configure here is compared against the value set in Max
hourly emails to determine whether an outgoing message should be
queued and resent later or discarded. For example, if you set this
value to 125%, then once the domain reaches its hourly limit, Exim
will queue any additional messages, up to 125% of the Max hourly
emails value. Once the account reaches 125% of the Max hourly emails
value, any additional outgoing messages are discarded.
You may use this feature to discard all outgoing messages once the
domain has reached its limit by setting the The percentage of email
messages (above the account’s hourly maximum) to queue and retry for
delivery value to 100.