Given a bit more time to tinker around I found the answer to both of my questions:
In order to modify the standard honeypot or to create your own, you have to extend the CommentForm
class by adding a clean_NAME_OF_HONEYPOT
function as well as a NAME_OF_HONEYPOT
variable both of which look similar to the standard ones and you also have to override the security_errors
function to include the name of your new/modified honeypot in the dictionary.
The best way to do this is to create your custom comments app as described here: https://docs.djangoproject.com/en/dev/ref/contrib/comments/custom/ .
I hope this answer helps anyone else in my situation.