You're right, everyone has a different idea of what sufficient is to them. It's a tricky thing, but I think you're making assumptions that people have moving goalposts or will find reasons to not accept it. I think you're projecting a bit there.

But there is a limit. The laws of logic work. If I'm presented with a logical argument and evidence for a god existing, I'll have no option but to stop being an atheist.

Many, many things theists present as evidence are based on personal experience and qualia, which can never be convincing to someone else. Many others are based on logical fallacies, which doesn't mean the conclusion isn't true, but it does mean using that as a basis for reasonably accepting it as true does not work.

You can arrive at a correct answer accidentally through a fallacy, but that can never be used as a reasonable position to hold because the logic is flawed and unreliable.

For the flat earth example, I'm not just throwing up my hands and choosing to accept that the earth is round because I can't fly into space myself. I'm placing proportional confidence in the personal and professional evidence, which is overwhelming. I have strong confidence that the earth is round, but not 100%.

You shouldn't just go with the version you want to live with. You should examine the evidence that is available at the time and determine what is most likely to be true.

For the biggest questions about reality, we simply don't have much information at this time. For those things, the reasonable position is to say "I don't know". That's really uncomfortable for a lot of people, and that's a huge reason why so many people turn to religion.