I think a solution is going to be less about changing minds, and more about changing incentives.
Meat-free food should be cheaper and easier. Walking into a supermarket or convenience store, one should be greeted with affordable, tasty, plant-based meals. The more affordable and accessible we make plant-based meals, the more people are going to eat them. And showing people that they can taste just as good as meat-based meals, will mean people won't immediately steer clear of them.