Thanks for linking to that Red Sails post -- that's what I had in mind. I think it significantly overstates its case.
Accept instead that they have been avoiding those truths for a reason. You were able to break through the propaganda barrier, and so could they if they really wanted to.
It's not that they could look past the propaganda if only they really wanted to, it's not even that they're avoiding the cracks in their worldview. They see the cracks, but they justify them in the manner I described above.
I think the way you get to reachable people is by attacking those justifications, not pointing to the cracks that they already see.
This has also been tried (the feasible version of it is mutual aid) without much success. The reasons it and other strategies have failed in the U.S. are (1) the repressive arm of the state is so strong, and (2) it's a rich enough country that trying to make it within the system is still a decent option for most people.
Now if we're talking offering them benefits the left can't actually deliver in the short term -- guaranteed housing, education, healthcare, etc. -- you have to go back to attacking their justifications for supporting the status quo. They aren't unaware of (for example) the problems for-profit healthcare causes, and they aren't willfully ignoring those problems, either. They justify it to themselves.