The reg form timer add-on includes detailed logging for failed registration attempts amongst other options.
As well as integration with StopBotters, a highly effective API which can also prevent registrations based on other criteria.
My recommendation is to turn the default registration timer off (set it to 0) and allow the add-on to do the timer bit.
Eventually the add on will remove the custom timer and leave the default and have all the logging API stuff alongside the default timer.