Non-religious but spiritual

Are you suggesting that morality can only be a result of religion?
No, not at all. Only that any moral system will be designed in the realm of ideas. That doesn't make it bad necessarily, but is that spirituality?
Is it your intent to move from religion to some other ideology?
If evolution is an ideology, yes.
Ok, thanks. My point would be that every ideology ever invented has come in to conflict with other ideologies, and more telling, also sub-divided in to internal warring factions. So even if an ideology is not religious, many of the same objectionable phenomena will present themselves. As example, some hard core atheists seem just as nutty as the hard core religious, and the fact that their ideologies are polar opposites seems not to matter.
From religion to experience?
Right. Religion is generally talk about experience. Jesus went in to the desert and had some experience. And then Jesus and lots of people started interpreting that experience, arguing about it, etc. "Religion to experience" might involve going in to the desert, having the experience, and then valuing the experience for itself, setting aside the process of interpretation. If an experience is "nutritious", who cares what it's called or what it means etc? As example here might be food. It's value does not depend on labels, analysis, interpretation etc.