Regulate the industries and trade, not people's behavior. It's much easier and you actually get results and people adapt to pricing by themselves. The reality is that we have a few billion people that are doing pretty well economically and they are going to be feeding themselves with whatever they can afford. Unless you can convince more than half of them to become vegans, that means demand for meat is going to go up, rather than down. A few privileged rich hipsters choosing to only eat food others can't afford is not going to be doing anything for this planet. It's not statistically meaningful. Not even close.
Industrial farming is the main problem here. We're literally eroding farmland by growing mono cultures (using pesticides, herbicides, fertilizers, etc) whose primary function is to feed cattle that spends all its life indoors turning this farm produce into manure. That in turn gets mixed with urine to produce a chemically very active mix that produces all sorts of nasty stuff. It's stupid and massively wasteful. It's only cheap because doing that is being subsidized and stimulated by governments. Stop doing doing that and the price of meat goes up and people adapt their behavior. Unsustainably produced cheap meat is the problem.
It's not the only way to produce meat but the it is the cheapest one and it's only cheap unless you also factor in the cost of destroying this planet. There are forms of farming that are effectively carbon negative (i.e. they capture more co2 than is released) that still produce meat and other produce. We can actually start undoing a lot of the damage already done simply by farming more smartly. This starts by stopping to reward harmful behavior with subsidies. Lots of farmers are already switching to more sustainable production methods because it makes business sense. Removing subsidies for their unsustainable competitors will help them.