One simple question

[Purple Rabbit]

Your method is not a 100% guarantee.

Nor did I say it was.

That's correct. And I did not say that you said it was.

My method is, however, consistent with reality thus far,...

That's circular reasoning because you really don't know for sure what reality is. It can only be consistent with your perception of reality. Needless to say that the same goes for me.

...without drawing fantastical conclusions, irrational elements, or unverifiable constructs. It isn't perfect, as my perception can be skewed. For this, self doubt is a necessary part of the equation.

I missed that self doubt in your question in the OP. If there was self-doubt shouldn't it have been stated thus: "How does one determine what is real and what is not real?"

For instance, all tests on the jar cannot absolutely rule out the possibility of a mind in a jar.

My method doesn't hope to absolutely rule out anything, but it can assess things by way of evidence. Acceptance is constructed upon evidence to support a certain assertion. A disembodied mind would have to be, by definition, a demonstrable element within that jar to be considered part of existence and reality.

If by this method you mean the scientific method, your method can only assess things up to a certain point, yes. So we agree it can never reach 100% accuracy. And we might agree that your and mine method not only fails at absolutely and definitely ruling out anything, it also fails at absolutely and definitely ruling in anything.

Who says that disembodiment is part of it. Maybe our bodies are just an illusion and always have been.

You're right that the mind in a jar as of yet is not within reach of measurement. And indeed that is a serious problem with it just as with the god concept. But those considerations are not about ultimate truth, it is nothing but a practical consideration. Even if we are in some Matrix, the reality that we can perceive is all we can make statements about, untill shown otherwise. This is a relative practical principle. Ultimate truth is not involved here.

Your question may be simple, but does it have a simple answer?

There is no right or wrong answer. It's not a trick question. I just want to get to why atheists and theists disagree on such a basic level.

There is no ultimate answer for both atheists and theists. In the end there only is a normative distinction in accepting or rejecting the scientific method.