I get that someone like Sam Harris, makes bank promoting his meditation app. But his atheist audience is very receptive.
It is certainly reasonable to argue about whether logic stands on its own without an observer, but not to doubt that there is a true world out there to be experienced.
I get the problem there; you're trying to teach what something feels like, and there just aren't words.
It's not surprising that you can alter the brain by various exercises, or that those exercises are counterintuitive. The brain is complicated and our tools for manipulating it are baroque. Still, it was a little weird to hear Harris give in without apparently reconsidering other forms of mental exercise from that standpoint.
Think of meditation more as a physical exercise for the brain, like yoga. Is yoga a religion, even if it strengthens your core? Many people do it without any religious ideas.
Same with breathing, 'low CO2' sounds bad, but we do have the next breath, the goals isn't continued low CO2, it can lead to increased oxygen later.
As to rationality. Meditation helps declutter thoughts, so that helps with rationality doesn't it? Why would being strung out and stressed be more rational?
Atheism means a lack of belief in a god. Just because many atheists go a step further or the word agnostic exists, that doesn't change the meaning.
I have yet to see an "official" source that says it's definitely belief of absence and not absence of belief. Agnosticism works just as well if you view it as subcategory of atheism.
Similar to what you said about me, I think you're perhaps putting faith/religious dogma and spirituality/holding things sacred in the same boat. I think having awe or wonder or a feeling of being part of something bigger is again orthogonal to belief in a particular god. I don't even think religion is the dividing line here - religion and ritual exists all over without an overarching deity.
I liked the underlying idea to what you said about motivation to explain away religious experience as physiological process; I think there is something interesting there. I expect this is a result of what people already believe, not a cause, but I like the concept of how people take in new information and default to directing it to "knowable, let's figure it out" or some version of "unknowable".
tl;dr - not believing in a god seems separate from spirituality and religious experience. Theist and atheist are extremely high level (and one dimensional) labels and there is a LOT of diverse (and overlapping) belief and experience under each.