See, when that pivot point hits, the conservatives I've known all either laugh it off or get angry. It's not "Oh wow, I actually agree with these points!", but "Ha ha, that's a neat trick, like asking someone for Pen 15" or "This damn dirty crypto-liberal is trying to trick me with his mind games!"
Practice helps. So does being a stranger that's visibly working class. I suspect you've run into a wall for being known and as a "hostile" for being a "liberal". My best success comes from when I can get around that, one on one. Got a former coworker who still goes to that evangelical church, but watches Democracy Now every day.
But also... Yeah, that happens. Sometimes it makes people question their ideas, sometimes we're sewing seeds for someone else to water. And that's okay.
In a very real way, we are talking about Christian-style evangelism.