You say you want to convince people "without having to shorten all of the freaking Inferential Distance". Yet you seem not to realize that to do so would be to practice a Dark Art.

Yes, exactly. Telling someone that the experiences which have convinced them of their religious beliefs aren't actually strong evidence for those beliefs requires explaining at minimum* Occam's Razor and Bayesian statistics. I've tried shortcuts, such as saying "it's just like how a patient is usually less qualified to diagnose their symptoms than a doctor," but that has never succeeded in conveying the message. If someone doesn't actually understand why entities shouldn't be multiplied beyond necessity and how to use evidence to evaluate claims, they're not going to accept what you say about their claims. We can keep trying to explain these concepts, and I do, but they have to decide they want to learn them.

*It's usually much more than just that, because religious people tend to come from a very anthropocentric worldview, where morality is objective, life has inherent meaning, human beings have souls, etc. We might speak the same language, but we're using very different systems of thought.

Edit to add: Eliezer has a very good post on this subject which makes the point better than I did: it's not enough just to cite Occam's Razor, Bayes' Theorem, etc.; there has to be understanding. Importantly, developing that understanding requires taking doubt seriously.

Even when it's explicitly pointed out, some people seemingly cannot follow the leap from the object-level "Use Occam's Razor! You have to see that your God is an unnecessary belief!" to the meta-level "Try to stop your mind from completing the pattern the usual way!"

...

If "Occam's Razor!" is your usual reply, your standard reply, the reply that all your friends give - then you'd better block your brain from instantly completing that pattern, if you're trying to instigate a true crisis of faith.

Better to think of such rules as, "Imagine what a skeptic would say - and then imagine what they would say to your response - and then imagine what else they might say, that would be harder to answer."

Or, "Try to think the thought that hurts the most."

And above all, the rule:

"Put forth the same level of desperate effort that it would take for a theist to reject their religion."