I think the real question is: can equivalent money to logging/beef be made from tropical forests? If we can come up with an answer to that, maybe we can revert this trend.
If we'd make it not economically useful to burn it down, because agricultural products were less profitable, that would work, probably.
So a simple economic solution to the problem is to stop buying so much beef and the deforestation would reduce drastically. Why would they continue to chop the forest down if they have no economic incentive to do so?
The excessive consumption of animal products in the west is the main reason why this "3 football fields" a minute thing is going on.
Generally, when people ask for an economic solution, they’re looking for a proposal to change behavioral incentives, rather than proclamation of the desirability of someone’s pet cause (as noble as it may be).
By reducing the amount of meat consumed in the west, there would be no reason to keep chopping down the forest, it's expensive.
In the west we would need a meat tax like it has been proposed in several countries, this alone we would reduce demand for beef and reduce the rate that the forest is getting chopped.
Only if it hurts on people's pockets will anything change, if it doesn't and it goes down for long enough, and the climate keep changing like it has it's going to end up as it as always ended when multiple groups of people are competing for resources: war.
Another one is "stop buying things you don't really need".
But yeah, good luck convincing people to get behind that.
Both of these are controversial subjects at best.
Have you seen the TV show Utopia? Basically a group of people decide it's in the humanity's best interest to wipe out 90% of the population with viruses. Rather grim, but understandable in a way.
While in the domain of Sci-Fi, the solution I liked better was the idea from "Forever peace" by John Haldeman, where human evolution is propelled to the next step by increasing mutual empathy through technology. The Internet might be a small step in that direction.
The faster we get people out of poverty, girls educated, and reduce child mortality, the faster we stop population growth.
All 3 have been curbed quite dramatically with a combination of regulation, graduated penalties and education. Yes there are gaps in enforcement, and these behaviors haven't been completely eradicated of course -- but dramatically curbed, nonetheless.
There's no reason the same can't happen with the current (wildly excessive) habit of read meat consumption.