Buddhism

it's definitely not scientistic or materialistic - i.e. it admits the possibility of unknowable aspects of reality.

A-theist just means without gods. Even "atheism" as a religious position is silent on the issue of, "Is what we can perceive all there is?" Even if most atheists aren't...

What if karma and/or reincarnation followed some multidimesional but still natural reality? Would that reduce your anxiety?

There's a difference between a life philosophy (such as compassion and non-attachment) and a cosmology (karma and reincarnation). IMO your thinking may go smoother if you tease those apart and address each on its own level. AFAIK there is no rule that says that Buddhism in general requires a cosmological component, unless you adhere to a particular school.

There are non-dualist relatives of Buddhism such as Taoism and Advaita that are even more open-ended.