I'm liberal. The loudest on the left have however, become insane. They're unreasonable, they're totalitarian and as OP raises, manipulating the masses through the media. As a libertarian lefty, the situation is as troubling to me as it is to you. So I'd be happy to help.
Lemchan's 5 ways to turn the tides and stop the Left from destroying us all
Don't call them "do-gooders", as you're aware it feeds into their hero complex. What I've been doing instead is referring to these types as "feel-gooders". Its more accurate, as they only care about things that make them feel good. On that note, don't go overboard. I see the route of ridicule tempting you. Ridicule has its places, such as in a meme or in a comic, in light articles, it may be very effective. However, be mindful that in an argument/discussion, it will likely backfire.
Conservatives should be mindful of their stereotypes and not feed into them. Also all need to be aware that all people view their own in-groups to be varied, but their out-groups as homogeneous. Put yourself, if you can, into an in group with those you're talking to. Find common ground and work from there. Otherwise you've given them the opportunity to pigeon hole you, they'll use it as an excuse to dismiss your arguments outright.
Understand that you cannot change someone's mind, all you can do is create enough cognitive dissonance that it forces them to re-evaluate their beliefs.
This means you must put your best arguments forward, with supporting evidence and try not to give way to your frustration. If the person you're challenging respects you then after the discussion they may reflect on what you said and begin looking into it independently. If they do start to come around be magnanimous about it.
More likely however, the person you're arguing with won't respect you. They will throw every illogical fallacy, ad hominem, appeal to emotion and ridicule that they can at you. In these instances, you're not trying to change their mind, but the minds of the audience. Poke holes in all of their arguments, don't allow them to keep the offensive, force them to defend.
The fastest way to make a feel-gooder fold is to ask them what their solution is. Once its all laid out, examine the consequences, and ask 'then what?' until they self-destruct. Doing things because they make you feel good is rarely a good long-term solution to a complex problem. Sometimes the world needs a 'bad guy' to make the hard and unpopular choices.
Speaking of bad guys...be aware of how people are manipulated using basic psychology. Look into Asch conformity experiments, and Milgram's obedience experiments. Knowledge of persuasion/compliance techniques may also be useful. I find the use of this knowledge for manipulating people to be distasteful and sort of evil--but you need to know about it because it is being used against you. For example, Facebook's OCC censorship campaign is attempting to use Asch's findings to force people into conformity.
You've already thought of this one but didn't say it straight. We need more sites to balance it out, and books, shows, youtube videos, etc. I'm working on this from my end, and hope others here are as well.