Logic tells me God doesn't exist but my heart says otherwise.

[Mudhammam]

I think atheism is mostly founded on principles of logic

That would be ideal...

But it seems to me-- and maybe I'm wrong-- that some kinds of powerful emotions and experiences also get discarded as meaningless or even deleterious.

Is that logical? I don't think so. You're right, we don't want to throw the baby out with the bath water... but being realistic, I don't think emotions are separable from any thought or action, including the exercise of logic; we naturally feel a sense of satisfaction when we are correctly applying logical principles or discovering where a fallacy in an argument lies. I think the division of logic and emotion, while you're probably right that some scientists and atheists have pretended it was possible, is an almost self-refuting fantasy, on par with one who believes that they're the only consciousness to *really* exist.

That's right. And yet if you ask people who found their world views on science or on the logical disregard of metaphysics if they meditate, or have an interest in lucid dreaming, OBEs, or experience a "communion with God" or any kind of metaphysical experience, you are much more likely to receive scorn than approval.

In red I have placed psychological phenomena that we know to exist (OBE not *actually* "being out of body," but clearly the illusion or hallucination of such experiences are as real as anything; I have never seen any convincing evidence that a person *actually* left their body and reported in precise detail events that were simultaneously occurring in some other location where the person was not present).
In blue we have obvious trouble making sense of what "communion with God" even means, not to mention there is zero evidence that God is anything more than projection of the ego or the wider, typically unnoticed, scope of subconscious feeling.

I've had some experiences that, while I don't want to attribute them to ghosts or gods, were certainly of that category that people usually call religious-- and whatever the true source of those experiences, they are an important part of my life and I feel I learned a lot from them. I think exploring the limits of what the mind can experience should be encouraged, but it's been my experienced that those who place logic at the center of their world view neither have the inclination to seek such experiences themselves, nor tolerance for those who do, nor even a fundamental understanding of what those experiences are like. Due to the limitations of their world view, they have missed out on experiences I have had myself, and cannot really understand what it is that they've missed, and refuse even to believe that they could have missed anything of value. They are wrong.

I don't doubt that through your experiences you can gain a much firmer understanding, even scientific knowledge of human nature and psychology; metaphysics, on the other hand? Highly unlikely. That would probably require a great deal of speculation and ad hoc assertions on your part, and wildly inconsistent claims or conclusions with similar reports of those types of experiences that others have. Perhaps we live in a pluralistic Universe where everybody's grandiose metaphysical statements possess an equal claim on reality; my experience, considering the utter failure of self-proclaimed soothsayers, prophets, divinities, etc. to possess any degree of reliable predictability or produce internally consistent reasons that correspond to any empirical data, is that this is not case.

It's one thing to refuse to make or accept factual assertions about what experiences really mean. But deliberately avoiding entire categories of experience is akin to an ostrich sticking its head in sand.

I don't think the situation requires that anyone needs to avoid "entire categories of experience." We simply need to approach these experiences as honestly and objectively as possible.