I think a decent chunk of people out there, 15-20% are going to ultimately be unreachable, no matter what approach people try to take. The damage is done. Trump just recently was at a rally in Alabama and tried to tell the attendees to get vaccinated because it's a good thing, and they booed Trump. Many people leaving the rally were interviewed and said they believe Trump never got the vaccine and just has to say that.
I sat in on some nursing meetings for a national health care company a few weeks back, and we had nurses from a few different states (including Florida) on there discussing policy changes regarding vaccine mandates at work, etc. It was honestly stunning to see how many nurses in a science-driven, medical profession were aggressively saying they weren't going to get vaccinated. Their primary reason appeared to be religious, with people openly saying in the meeting they think God is going to protect them from the virus (I guess all the dead people so far just weren't worthy), and then listing a dozen different conspiratorial concerns about the vaccine. Nurses, in a meeting at work (why even be a nurse if you think God takes care of all diseases?).
My point is that for a lot of people it's not really a rational discussion anymore. It's part of their religious conviction, or part of their political identity, and they're just as likely now to be persuaded to get vaccinated as they are likely to be persuaded to switch political parties. People have tried waiting 9 months, tried giving them money, tried paying for the vaccine and offering it for free, tried appeals from celebrities, republicans and democrats. Tried appeals from physicians. Tried appeals from ex-vaccine skeptics that ended up in the ICU and tell their story on the news about how they wish they got it.
The reality is that this last chunk of hardline anti-vaxers are fundamentalists in their beliefs, and ultimately I don't think we'll have a choice but to ban them from places of high risk; like, airports, public schools, certain jobs (including teachers, police, military, health care, and more).
Hopefully some of the people on the fence that were casually hesitant will decide to do the right thing, but a decent chunk of the people left probably never will. I don't really want to waste time thinking about how people feel about it, or what specific psychological tactic might finally convince people to get a free vaccine. At this point, they are free to not get it, but we should just limit the amount of damage they can do to others. I think 1 unvaccinated teacher recently just spread to 50 kids, and we'll continue to see stories like that going forward. Do I care about what might have finally convinced that teacher? At this point, not really. I think they just need to mandate it for teachers and just be done with it, and she can decide what she wants to do.
I'd rather that businesses didn't have to step in with this kind of measure, but we have proven as a society that nothing else is going to work at this point. The damage is done. Our health officials destroyed a lot of their credibility with flip-flopping mask statements, or media has destroyed their credibility on nearly everything for years, our previous president instilled a base sentiment of mask and vaccine skepticism that was embraced by his most hardcore fans, then that was fused with religious elements and churches and pastors have run with it. COVID's initial skepticism also happened at the same time as stop the steal movements, and BLM protests and got further politicized. I don't think that can all be undone. Even with all those huge mistakes, the government and businesses are not going to just sit around and watch people die and be put at risk and not do anything. They're going to keep slowly increasing the mandates, because that's really all that's left. And the sad thing is, ultimately the mandates will work. People will cave and go get their shot, and go to work, and life will go on.