That is just another arms race. I think it naïve to assume that people can be educated out of this problem. Some people can be, but large numbers will always fall for a good hoax. What we need is laws and policies to address the problem. The good news is that this problem is nothing new. The laws are already on the books.
Imho this is something that the law can manage so long as the legal system is allowed to run its course. People publishing true deepfakes, not parodies but actual attempts to fool people, should face the same slander and defamation charges that previous fakes have for centuries. Even copyright law has tests to draw lines between legitimate parody and improper fakery. Hustler v. Falwell (the Larry Flint case) was about a literary deepfake, a sham interview in a porn magazine. Those who take deepfake too far, or republish such material, open themselves to legal attack. Let the lawyers do their thing.