Too often barbarians have overrun naively-managed Internet forums ;-)
I seek forum management software that
features practical, effective facilities to exclude, marginalize and/or fight the aforementioned barbarians
I'm surprised that (since you know StackExchange) that you do not know Discourse
(BTW You talk about 'forum management' software which I assume to be 'forum software')
Discourse has a voting/rating system, you can flag bad questions etc. Here is the FAQ.
More importantly, it was developed with exactly your concerns in mind: how can we make sure we have constructive dialogs? That's why they call it a Civilized Discourse Construction Kit ;-)
You should read e.g. this blog post and this one to get an idea of the thoughts behing Discourse.
You can try their sandbox (register first).
BTW Although you can set it up yourself, they also have a very reasonable hosting offer: $99 for a one-time install, plus a $10/month hosting fee.
(No, I'm not in any way affiliated, but enthusiastic, and planning to use it in an upcoming project).
If you are looking for a StackExchange like Question and Answers open-source software, you might take a look at biostars.org. The software running the site is open source, based on Django/Python, and could do what you ask for: upvote or down-vote questions or answers and use a reputation system for the users.
Another solution you may want to look at (which is open source) is based on Drupal, for which these add-ons exist to make it do what you are looking for:
A question/answer site built to emulate the core functionality of sites on the StackExchange platform, such as:
There is a Drupal theme for it, i.e the ArrayShift Theme. Here is a screenshot (from its project pages):
It has been in a kind of unsupported status until recently, though the updated project page contains a roadmap to get it going again for D7 (and D8 later on).
Disclosure: I'm the (new) maintainer of ArrayShift (and its related modules and theme).