The problem you're missing is that there really aren't a significant number of people "on the fence" any more.
There are some anti-vaxxers who say, as a rhetorical device in order to project the illusion of thoughtfulness, that they're "on the fence" ... but they're really not.
I spent a good year or so "engaging" people on a firearms forum I frequent, and they're unteachable.
This morning I looked in on a couple of their COVID threads and they're still posting straight up echo-chamber lies like "everybody knows the virus is an engineered bioweapon" and "CDC ran the gain-of-function research at the Wuhan lab" and "Fauci gets royalties from his vaccine patents" and "Biden is a Xi puppet pushing vaccines to cull the world population of old people" and "Bill Gates wants to kill 20% of the world population to stop global warming" and "doctors are systemically lying about COVID numbers because they get paid more for COVID cases than _____" ... they use words like plandemic, Dr Fauxi, express disdain for actual expertise and education ...
All of these lies are things that have been carefully, competently, eloquently refuted 1000s of times by the media, by the CDC, by the government, by doctors, by ordinary people like us on forums or Facebook. And they still believe it.
At some point you've got to quit pretending that all opinions are equally valid, and deserving of a respectful listen. These aren't bad people. They're sincere. They might not even be dumb people - though if you look up "dumb" in a dictionary, you'll probably find words to the effect of "difficulty processing and understanding new information." So yeah, if I'm honest, I have to admit I think most of them are actually dumb. Regardless, they aren't people worth engaging any more.
Engage if you want, fight the good fight if you want, but these people will never get the vaccine or even admit the pandemic is real. At this point the focus should be on managing the pandemic as best we can, given the obstacles they put up. Because those obstacles aren't ever going to go away.