often other people are present who are not so dug in
That's a really important dynamic. I've had several of these types of conversations swing my way because I was able to persuade the undecided people who were there. That's part of the tribal approval mechanism. Seeing someone else agree grants psychological permission to agree.
The other thing I thought of is that it's not really relevant what works best on most people, if they aren't going to be receptive anyway. Your direct/confrontational approach might actually be extremely effective on the set of people who can be reached. It's definitely what works on me.